A.T. Fomenko's Books

History: fiction or science?. Chronology 1

By: A. T. Fomenko

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History: fiction or science?. Chronology 1

By: A. T. Fomenko

The author contends that all generaly accepted historical chronology prior to the 16th century is inaccurate, often off by many hundreds or even thousands of years. Volume 1 of a proposed seven volumes.

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634

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Mithec

Published Date

ISBN 10

2913621074

ISBN 13

9782913621077

Integrable Hamiltonian Systems

Geometry, Topology, Classification

By: A.V. Bolsinov,A.T. Fomenko

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Integrable Hamiltonian Systems

Geometry, Topology, Classification

By: A.V. Bolsinov,A.T. Fomenko

Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

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752

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CRC Press

Published Date

ISBN 10

0203643429

ISBN 13

9780203643426

Variational Problems in Topology

The Geometry of Length, Area and Volume

By: A.T. Fomenko

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Variational Problems in Topology

The Geometry of Length, Area and Volume

By: A.T. Fomenko

Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.

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290

Publisher

Routledge

Published Date

ISBN 10

1351405675

ISBN 13

9781351405676

Geometrical and Statistical Methods of Analysis of Star Configurations Dating Ptolemy's Almagest

By: A.T. Fomenko

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Geometrical and Statistical Methods of Analysis of Star Configurations Dating Ptolemy's Almagest

By: A.T. Fomenko

This easy-to-follow book offers a statistico-geometrical approach for dating ancient star catalogs. The authors' scientific methods reveal statistical properties of ancient catalogs and overcome the difficulties of their dating originated by the low accuracy of these catalogs. Methods are tested on reliably dated medieval star catalogs and applied to the star catalog of the Almagest. Here, the dating of Ptolemy's famous star catalog is reconsidered and recalculated using modern mathematical techniques.The text provides necessary information from astronomy and astrometry. It also covers the history of observational equipment and methods for measuring coordinates of stars. Many chapters are devoted to the Almagest, from a preliminary analysis to a global statistical processing of the catalog and its basic parts. Mathematics are simplified in this book for easy reading. This book will prove invaluable for mathematicians, astronomers, astrophysicists, specialists in natural sciences, historians interested in mathematical and statistical methods, and second-year mathematics students.Features:

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311

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CRC Press

Published Date

ISBN 10

1351080709

ISBN 13

9781351080705

Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem

By: A. T. Fomenko

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Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem

By: A. T. Fomenko

Plateau's problem is a scientific trend in modern mathematics that unites several different problems connected with the study of minimal surfaces. In its simplest version, Plateau's problem is concerned with finding a surface of least area that spans a given fixed one-dimensional contour in three-dimensional space--perhaps the best-known example of such surfaces is provided by soap films. From the mathematical point of view, such films are described as solutions of a second-order partial differential equation, so their behavior is quite complicated and has still not been thoroughly studied. Soap films, or, more generally, interfaces between physical media in equilibrium, arise in many applied problems in chemistry, physics, and also in nature. In applications, one finds not only two-dimensional but also multidimensional minimal surfaces that span fixed closed ``contours'' in some multidimensional Riemannian space. An exact mathematical statement of the problem of finding a surface of least area or volume requires the formulation of definitions of such fundamental concepts as a surface, its boundary, minimality of a surface, and so on. It turns out that there are several natural definitions of these concepts, which permit the study of minimal surfaces by different, and complementary, methods. In the framework of this comparatively small book it would be almost impossible to cover all aspects of the modern problem of Plateau, to which a vast literature has been devoted. However, this book makes a unique contribution to this literature, for the authors' guiding principle was to present the material with a maximum of clarity and a minimum of formalization. Chapter 1 contains historical background on Plateau's problem, referring to the period preceding the 1930s, and a description of its connections with the natural sciences. This part is intended for a very wide circle of readers and is accessible, for example, to first-year graduate students. The next part of the book, comprising Chapters 2-5, gives a fairly complete survey of various modern trends in Plateau's problem. This section is accessible to second- and third-year students specializing in physics and mathematics. The remaining chapters present a detailed exposition of one of these trends (the homotopic version of Plateau's problem in terms of stratified multivarifolds) and the Plateau problem in homogeneous symplectic spaces. This last part is intended for specialists interested in the modern theory of minimal surfaces and can be used for special courses; a command of the concepts of functional analysis is assumed.

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424

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American Mathematical Soc.

Published Date

ISBN 10

0821898272

ISBN 13

9780821898277

Basic Elements of Differential Geometry and Topology

By: S.P. Novikov,A.T. Fomenko

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Basic Elements of Differential Geometry and Topology

By: S.P. Novikov,A.T. Fomenko

One service mathematics has rendered the 'Et moi ..., si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Matht"natics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series

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500

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401578958

ISBN 13

9789401578950

Mathematical Impressions

By: A. T. Fomenko

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Mathematical Impressions

By: A. T. Fomenko

Soviet mathematician Fomenko augments his technical books and papers with visual impressions of mathematical concepts, often reminiscent of Escher, and with allusions to Breughel and Durer. Over 80 reproductions, a few in color, are accompanied by the artist's explanation of the mathematical principles being suggested. Annotation copyrighted by Book News, Inc., Portland, OR

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202

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American Mathematical Soc.

Published Date

ISBN 10

0821801627

ISBN 13

9780821801628

History, Fiction Or Science?

Chronology

By: A. T. Fomenko

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History, Fiction Or Science?

Chronology

By: A. T. Fomenko

The author posits that all generally accepted chronology before the 16th century is in error by hundreds or thousands of years.

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562

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Mithec

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ISBN 10

2913621066

ISBN 13

9782913621060

Modern Geometry - Methods and Applications

Part 3: Introduction to Homology Theory

By: B. A. Dubrovin,Boris Anatolʹevich Dubrovin,A. T. Fomenko,Sergeĭ Petrovich Novikov

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Modern Geometry - Methods and Applications

Part 3: Introduction to Homology Theory

By: B. A. Dubrovin,Boris Anatolʹevich Dubrovin,A. T. Fomenko,Sergeĭ Petrovich Novikov

Part II. The geometry and topology of manifolds. This is the second volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include homotopy groups, fibre bundles, dynamical systems, and foliations. The exposition is simple and concrete, and in a terminology palatable to physicists.

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432

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Springer Science & Business Media

Published Date

ISBN 10

0387972714

ISBN 13

9780387972718

Integrable Systems on Lie Algebras and Symmetric Spaces

By: A. T. Fomenko,V. V. Trofimov

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Integrable Systems on Lie Algebras and Symmetric Spaces

By: A. T. Fomenko,V. V. Trofimov

Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR

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316

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CRC Press

Published Date

ISBN 10

2881241700

ISBN 13

9782881241703

Variational Problems in Topology

The Geometry of Length, Area and Volume

By: A.T. Fomenko

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Variational Problems in Topology

The Geometry of Length, Area and Volume

By: A.T. Fomenko

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226

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Routledge

Published Date

ISBN 10

1351405683

ISBN 13

9781351405683

History, Fiction Or Science?

Chronology

By: Anatoly T. Fomenko

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History, Fiction Or Science?

Chronology

By: Anatoly T. Fomenko

Anatoly Fomenko's revisionist chronology of world history, which argues that the accepted chronology of world history is fundamentally in error, and that events attributed to ancient times actually occurred during the Middle Ages.

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624

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ISBN 10

2913621058

ISBN 13

9782913621053

Mathematical Impressions

By: A. T. Fomenko

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Mathematical Impressions

By: A. T. Fomenko

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202

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American Mathematical Soc.

Published Date

ISBN 10

0821801627

ISBN 13

9780821801628

Crusades and Exoduses

By: A. T. Fomenko

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Crusades and Exoduses

By: A. T. Fomenko

The most probable prototype of the historical Jesus was Andronikos I Komnenos (allegedly AD 1183 to 1185), the Emperor of Byzantine, reflected in the consensual history for his numerous failed reforms; his traits and deeds reflected in 'biographies' of many real and imaginary persons. According to New Chronology, the New Testament is the rendition of religious events of the XIIth century AD. Crusades of 1189-1192 AD and 1199-1204 AD to Jerusalem-Constantinople were military operations under the banner of Christianity by the followers and relatives of Jesus idem Emperor Andronicus killed during a religious mutiny. Crusades have ended with the Sack of Constantinople in 1204. The historical Jesus Christ is a composite figure and reflection of the Bible prophet Elisha, Osiris, god of the death, life, and resurrection, Pope Gregory VII, Saint Basil of Caesarea, and even Li Yuanhao ("Son of Heaven"), Euclides, Dionysius and Andronikos I Komnenos the emperor of Byzantine. The seemingly vast differences in the biographies of these figures result from a difference in languages. The consensual world history was manufactured in Europe in XVI-XIX centuries with political agenda of powers of that period on the basis of erroneous chronology elaborated by Jesuits Joseph Justus Scaliger and Dionysius Petavius. - By the middle of XVI th century the prime political agenda of Europe that reached superiority in Sciences and Technologies, but was still inferior militarily to the Evil Empire of Eurasia, was to free Europe. - The concerted effort of European aristocracy, black and white Catholic clergy, Protestants, humanists and scientists in XV - XVII th centuries in creation and dissemination of fictional Ancient World served this agenda. - The fictional Ancient World was created by representing events of XI-XVI centuries as ones that happened thousands of years before according to the ancient sources they wrote by authorities they invented. - The European aristocracy, a considerable part of which were fugitives from Byzantine and/or the inheritors of Eurasian warlords, supported the myth of Ancient World to justify its claims to countries they ruled. - The black and white Catholic clergy, Protestants developed and supported the myth of Ancient World to justify their claims of being more ancient and to separate themselves from Eurasian orthodoxy in the countries ruled by European aristocracy. - The scientists supported the myth of Ancient World as safe cover for their heretic research that produced results contrarian to the tenets of Christianity. They justified their discoveries by authorities of ancient scientists they themselves invented and used as pseudonyms. - The humanists developed and supported the myth of Ancient World as a cozy safe haven for their ideas that conflicted with Christianity and aristocracy. They disguised and justified their ideas on authorities of ancient authors of their own making and wrote under their glorious aliases. Saint Augustin being prescient said .."beware of mathematicians, especially when they speak the truth!

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200

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Createspace Independent Publishing Platform

Published Date

ISBN 10

1977933572

ISBN 13

9781977933577

Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

manifolds, transformation groups, and Lie algebras, as well as the basic concepts of visual topology. It was also agreed that the course should be given in as simple and concrete a language as possible, and that wherever practic able the terminology should be that used by physicists. Thus it was along these lines that the archetypal course was taught. It was given more permanent form as duplicated lecture notes published under the auspices of Moscow State University as: Differential Geometry, Parts I and II, by S. P. Novikov, Division of Mechanics, Moscow State University, 1972. Subsequently various parts of the course were altered, and new topics added. This supplementary material was published (also in duplicated form) as Differential Geometry, Part III, by S. P. Novikov and A. T. Fomenko, Division of Mechanics, Moscow State University, 1974. The present book is the outcome of a reworking, re-ordering, and ex tensive elaboration of the above-mentioned lecture notes. It is the authors' view that it will serve as a basic text from which the essentials for a course in modern geometry may be easily extracted. To S. P. Novikov are due the original conception and the overall plan of the book. The work of organizing the material contained in the duplicated lecture notes in accordance with this plan was carried out by B. A. Dubrovin.

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479

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Springer Science & Business Media

Published Date

ISBN 10

1468499467

ISBN 13

9781468499469

Minimal Surfaces

By: A. T. Fomenko

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Minimal Surfaces

By: A. T. Fomenko

This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas: one-dimensional minimal graphs on Riemannian surfaces and the Steiner problem, two-dimensional minimal surfaces and surfaces of constant mean curvature in three-dimensional Euclidean space, and multidimensional globally minimal and harmonic surfaces in Riemannian manifolds. The volume opens with an exposition of several important problems in the modern theory of minimal surfaces that will be of interest to newcomers to the field. Prepared with attention to clarity and accessibility, these papers will appeal to mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.

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364

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American Mathematical Soc.

Published Date

ISBN 10

0821841165

ISBN 13

9780821841167

Elements of the geometry and topology of minimal surfaces in three-dimensional space

By: A. T. Fomenko,A. A. Tuzhilin

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Elements of the geometry and topology of minimal surfaces in three-dimensional space

By: A. T. Fomenko,A. A. Tuzhilin

This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.

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156

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American Mathematical Soc.

Published Date

ISBN 10

0821837915

ISBN 13

9780821837917

Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

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447

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Springer Science & Business Media

Published Date

ISBN 10

146121100X

ISBN 13

9781461211006

Integrability and Nonintegrability in Geometry and Mechanics

By: A.T. Fomenko

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Integrability and Nonintegrability in Geometry and Mechanics

By: A.T. Fomenko

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. 1hen one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin' . • 1111 Oulik'. n. . Chi" •. • ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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358

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Springer Science & Business Media

Published Date

ISBN 10

9400930690

ISBN 13

9789400930698

Geometrical and Statistical Methods of Analysis of Star Configurations Dating Ptolemy's Almagest

By: A.T. Fomenko

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Geometrical and Statistical Methods of Analysis of Star Configurations Dating Ptolemy's Almagest

By: A.T. Fomenko

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311

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CRC Press

Published Date

ISBN 10

1351080709

ISBN 13

9781351080705

Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating

Volume I: The Development of the Statistical Tools

By: A.T. Fomenko

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Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating

Volume I: The Development of the Statistical Tools

By: A.T. Fomenko

Today the methods of applied statistics have penetrated very different fields of knowledge, including the investigation oftexts ofvarious origins. These "texts" may be considered as signal sequences of different kinds, long genetic codes, graphic representations (which may be coded and represented by a "text"), as well as actual narrative texts (for example, historical chronicles, originals, documents, etc. ). One ofthe most important problems arising here is to recognize dependent text, i. e. , texts which have a measure of "resemblance", arising from some kind of "common origin". For instance, in pattern-recognition problems, it is essential to identify from a large set of "patterns" a pattern that is "closest" to a given one; in studying long signal sequences, it is important to recognize "homogeneous subsequences" and the places of their junction. This includes, in particular, the well-known change-point prob lern, which is given considerable attention in mathematical statistics and the theory of stochastic processes. As applied to the study of narrative texts, the problern of recognizing depen dent and independent texts ( e . g. , chronicles) Ieads to the problern offinding texts having a common source, i. e. , the sameoriginal (such texts are naturally called dependent), or, on the contrary, having different sources (such texts are natu rally called independent). Clearly, such problems are exceedingly complicated, and therefore the appearance of new empirico-statistical recognition methods which, along with the classical approaches, may prove useful in concrete studies (e. g. , source determination) is welcome.

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