Michel Demazure's Books

Bifurcations and Catastrophes

Geometry of Solutions to Nonlinear Problems

By: Michel Demazure

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Bifurcations and Catastrophes

Geometry of Solutions to Nonlinear Problems

By: Michel Demazure

Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.

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Page Count

304

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642571344

ISBN 13

9783642571343

Frobenius Splitting Methods in Geometry and Representation Theory

By: Michel Brion,Shrawan Kumar

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Frobenius Splitting Methods in Geometry and Representation Theory

By: Michel Brion,Shrawan Kumar

Systematically develops the theory of Frobenius splittings and covers all its major developments. Concise, efficient exposition unfolds from basic introductory material on Frobenius splittings—definitions, properties and examples—to cutting edge research.

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Page Count

259

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817644059

ISBN 13

9780817644055

Introduction to Complex Reflection Groups and Their Braid Groups

By: Michel Broué

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Introduction to Complex Reflection Groups and Their Braid Groups

By: Michel Broué

This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.

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Page Count

150

Publisher

Springer

Published Date

ISBN 10

3642111750

ISBN 13

9783642111754

Symplectic Geometry and Analytical Mechanics

By: P. Libermann,Charles-Michel Marle

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Symplectic Geometry and Analytical Mechanics

By: P. Libermann,Charles-Michel Marle

Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' Brown 'The point of a Pin'. in R. van Gulik's The Chinese Maze Murders. 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 thouglit to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sci ences has changed drastically in recent years: measure theory is used (non-trivially) in re gional 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 homo topy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

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Page Count

541

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400938071

ISBN 13

9789400938076

Scale Invariance

From Phase Transitions to Turbulence

By: Annick LESNE,Michel Laguës

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Scale Invariance

From Phase Transitions to Turbulence

By: Annick LESNE,Michel Laguës

During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.

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Page Count

406

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364215123X

ISBN 13

9783642151231

Control Theory for Engineers

A Primer

By: Brigitte d'Andréa-Novel,Michel De Lara

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Control Theory for Engineers

A Primer

By: Brigitte d'Andréa-Novel,Michel De Lara

Control Theory is at the heart of information and communication technologies of complex systems. It can contribute to meeting the energy and environmental challenges we are facing. The textbook is organized in the way an engineer classically proceeds to solve a control problem, that is, elaboration of a mathematical model capturing the process behavior, analysis of this model and design of a control to achieve the desired objectives. It is divided into three Parts. The first part of the text addresses modeling aspects through state space and input-output representations. The notion of the internal state of a system (for example mechanical, thermal or electrical), as well as its description using a finite number of variables, is also emphasized. The second part is devoted to the stability analysis of an equilibrium point. The authors present classical tools for stability analysis, such as linearization techniques and Lyapunov functions. Central to Control Theory are the notions of feedback and of closed-loop, and the third part of the textbook describes the linear control synthesis in a continuous and discrete-time framework and also in a probabilistic context. Quadratic optimization and Kalman filtering are presented, as well as the polynomial representation, a convenient approach to reject perturbations on the system without making the control law more complex. Throughout the text, different examples are developed, both in the chapters and in the exercises.

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Page Count

299

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642343244

ISBN 13

9783642343247

The p-adic Simpson Correspondence (AM-193)

By: Ahmed Abbes,Michel Gros,Takeshi Tsuji

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The p-adic Simpson Correspondence (AM-193)

By: Ahmed Abbes,Michel Gros,Takeshi Tsuji

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.

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Page Count

618

Publisher

Princeton University Press

Published Date

ISBN 10

1400881234

ISBN 13

9781400881239

Bifurcations and Catastrophes

Geometry of Solutions to Nonlinear Problems

By: Michel Demazure

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Bifurcations and Catastrophes

Geometry of Solutions to Nonlinear Problems

By: Michel Demazure

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Write a review

Solve jigsaw puzzle

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Page Count

304

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642571344

ISBN 13

9783642571343

Book's by Michel Demazure

Bifurcations and Catastrophes

Bifurcations and Catastrophes

Frobenius Splitting Methods in Geometry and Representation Theory

Frobenius Splitting Methods in Geometry and Representation Theory

Introduction to Complex Reflection Groups and Their Braid Groups

Introduction to Complex Reflection Groups and Their Braid Groups

Symplectic Geometry and Analytical Mechanics

Symplectic Geometry and Analytical Mechanics

Scale Invariance

Scale Invariance

Control Theory for Engineers

Control Theory for Engineers

The p-adic Simpson Correspondence (AM-193)

The p-adic Simpson Correspondence (AM-193)

Bifurcations and Catastrophes

Bifurcations and Catastrophes

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