This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this research has increased. Therefore the book purpose is to give a global presentation of a matter, available till now only in a partial form. Fundamental notions and tools (such as “critical manifolds”), as the most part of results, are accompanied by many examples and figures.
The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.
The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.
Ermanna Montanari: a minute body that grows enormous on stage and a magnetic visage capable of expressing unlimited intensities; a voice that creates stage figures and becomes a musical instrument; an original language that encompasses every type of performance; microscopic precision and the magma of an infancy still vital in the language of dreams and the enigma of her native dialect. Laura Mariani, subtle analyst of theater and memory, portrays Ermanna in the weaving of art and life and in relation to Marco Martinelli, director and playwright and other pole in a complex alchemy. Mariani interrogates the figure of Ermanna through written and visual sources, unpublished notebooks and traces of the process of creation. A narrative journey—biography, portrait of the artist, chronicle of becoming—to examine in detail the raw material of an actress and of theater as it unfolds.
A comprehensive, full-color guide to the principles and practice of neuropsychiatry and behavioral neurology. A primary resource in the field A Doody's Core Title for 2023! From the world-renowned experts at the Center for Brain/Mind Medicine at Brigham and Women’s Hospital and Harvard Medical School, Neuropsychiatry and Behavioral Neurology delivers authoritative, multidisciplinary information and insights for improving patient care. Chapter authors include additional worldwide academic clinician leaders from sister institutions. Covering the latest advances in cognitive, affective, and behavioral neuroscience, the text provides a practical and clearly written approach to structural and functional neuroanatomy; neuropsychiatric and behavioral neurology assessments and treatments; and neurobehavioral/neuropsychiatric syndromes and disorders. Neuropsychiatry and Behavioral Neurology includes: A definitive introductory chapter on the neuroanatomy of cognitive and behavioral neuroscience Chapters on the neurocircuitry of emotions and cognition Chapters on neuropsychiatric assessment methods and therapeutics, including pharmacology and neurostimulation modalities Chapters on neurobehavioral and neuropsychiatric syndromes, as well as on neuropsychiatric aspects of different neurological and medical diseases Numerous full-color illustrations of brain anatomy High-resolution brain CT and MRI scans Summaries and key points, patient cases, and multiple choice questions with annotated answers Evidence-based updates, combined with clinical guidance from master academic clinician Whether you’re a trainee, recent graduate, seasoned practicing clinician, or investigator interested in linking basic neuroscience research to clinical care, you’ll find everything you need to determine the neurobiological origins of alterations in emotion, cognition, and behavior; contextualize the illness to emphasize the role of underlying brain circuitry; develop informed differential diagnoses; and plan and implement the most effective treatment strategies. This text meets the curriculum requirements needed to prepare for board certification in Behavioral Neurology and Neuropsychiatry.
This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this research has increased. Therefore the book purpose is to give a global presentation of a matter, available till now only in a partial form. Fundamental notions and tools (such as “critical manifolds”), as the most part of results, are accompanied by many examples and figures.
The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent map and its application as a border collision normal form are discussed. We describe the period adding and incrementing bifurcation structures in the domain of regular dynamics of a discontinuous piecewise-linear map, and the related bandcount adding and incrementing structures in the domain of robust chaos. Also, we explain how these structures originate from particular codimension-two bifurcation points which act as organizing centers. In addition, we present the map replacement technique which provides a powerful tool for the description of bifurcation structures in piecewise-linear and other form of invariant maps to a much further extent than the other approaches.
The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.
Chaos in Discrete Dynamical Systems covers topics in chaos theory, bifurcations and critical curves in a visual, 2-dimensional context. This unique publication is the culmination of a three-year experiment in electronic publishing. As such, it is a package comprised of three carefully intertwined components: a printed book, a cross-platform CD-ROM and a website. The extensively illustrated book is the primary component. The CD-ROM is mainly devoted to presenting 12 computer graphic animations in full color, all tied directly into the content of the book. The user interface to the CD-ROM is made in the style of the world wide web. It is designed to integrate seamlessly with the web site dedicated to this project. This site is maintained by the Visual Math Institute, UC Santa Cruz: http://www.vismath.org/chaos. Motivation for this ambitious package is the conviction that this style of electronic publishing is the ideal medium for mathematical communication. This is especially true for the branch of mathematics known as dynamical systems theory. The essence of this communicative style is the dynapic technique, in which a drawing is developed stroke-by-stroke, along with a carefully coordinated spoken commentary. This is the traditional method used by most mathematicians when speaking among themselves. Visual Math!
Continues the author's story of personal crises, highlighted by the irony and humor that paralleled her professional triumph, and includes anecdotes of the famous and infamous
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