Search results for: global-theory-of-dynamical-systems

Global Theory of Dynamical Systems

Author : Z. Nitecki
File Size : 76.83 MB
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Global Theory of Dynamical Systems

Author : Z. Nitecki
File Size : 34.83 MB
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Global Theory of Dynamical Systems

Author : Zbigniew H. Nitecki
File Size : 33.65 MB
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Nielsen Theory and Dynamical Systems

Author : Christopher Keil McCord
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This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Nielsen Theory and Dynamical Systems, held in June 1992 at Mount Holyoke College. Focusing on the interface between Nielsen fixed point theory and dynamical systems, this book provides an almost complete survey of the state of the art of Nielsen theory. Most of the articles are expository, making them accessible to both graduate students and researchers in algebraic topology, fixed point theory, and dynamical systems.

Geometric Theory of Dynamical Systems

Author : J. Jr. Palis
File Size : 90.8 MB
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... cette etude qualitative (des equations difj'erentielles) aura par elle-m me un inter t du premier ordre ... HENRI POINCARE, 1881. We present in this book a view of the Geometric Theory of Dynamical Systems, which is introductory and yet gives the reader an understanding of some of the basic ideas involved in two important topics: structural stability and genericity. This theory has been considered by many mathematicians starting with Poincare, Liapunov and Birkhoff. In recent years some of its general aims were established and it experienced considerable development. More than two decades passed between two important events: the work of Andronov and Pontryagin (1937) introducing the basic concept of structural stability and the articles of Peixoto (1958-1962) proving the density of stable vector fields on surfaces. It was then that Smale enriched the theory substantially by defining as a main objective the search for generic and stable properties and by obtaining results and proposing problems of great relevance in this context. In this same period Hartman and Grobman showed that local stability is a generic property. Soon after this Kupka and Smale successfully attacked the problem for periodic orbits. We intend to give the reader the flavour of this theory by means of many examples and by the systematic proof of the Hartman-Grobman and the Stable Manifold Theorems (Chapter 2), the Kupka-Smale Theorem (Chapter 3) and Peixoto's Theorem (Chapter 4). Several ofthe proofs we give vii Introduction Vlll are simpler than the original ones and are open to important generalizations.

Stability Theory of Dynamical Systems

Author : N.P. Bhatia
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Reprint of classic reference work. Over 400 books have been published in the series Classics in Mathematics, many remain standard references for their subject. All books in this series are reissued in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. "... The book has many good points: clear organization, historical notes and references at the end of every chapter, and an excellent bibliography. The text is well-written, at a level appropriate for the intended audience, and it represents a very good introduction to the basic theory of dynamical systems."

Fundamentals of Dynamical Systems and Bifurcation Theory

Author : Milan Medved̕
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This graduate level text explains the fundamentals of the theory of dynamical systems. After reading it you will have a good enough understanding of the area to study the extensive literature on dynamical systems. The book is self contained, as all the essential definitions and proofs are supplied, as are useful references: all the reader needs is a knowledge of basic mathematical analysis, algebra and topology. However, the first chapter contains an explanation of some of the methods of differential topology an understanding of which is essential to the theory of dynamical systems. A clear introduction to the field, which is equally useful for postgraduates in the natural sciences, engineering and economics.

Global Theory of Dynamical Systems

Author : Z. Nitecki
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Lectures on Dynamical Systems Structural Stability and Their Applications

Author : Kotik K Lee
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The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems. Contents:IntroductionTopics in Topology and Differential GeometryIntroduction to Global Analysis and Infinite Dimensional ManifoldsGeneral Theory of Dynamical SystemsStability Theory and Liapunov's Direct MethodIntroduction to the General Theory of Structural StabilityApplications Readership: Applied mathematicians and engineers. Keywords:Asymptotically Stable;Bifurcation;Dispersive Systems;Global Analysis;Integral Flow;Liapunov Functions;Linearization;Nonlinear Dynamical Systems;Stable Manifolds;Structural StabilityReview:“The author's style is clear, formulations of mathematical results are precise … The book helps the reader to create a good global picture of the theory of dynamical systems. The author has gathered a considerable number of facts about dynamical systems in this book, including almost 1000 references, so that it can also serve as a handbook for mathematicians beginning to work in this area … The book is useful not only for technicians, but also for mathematicians, and we recommend it to anyone working in dynamical systems.”Alois Klíc Mathematical Reviews

An Introduction to Infinite Dimensional Dynamical Systems Geometric Theory

Author : J.K. Hale
File Size : 55.96 MB
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Including: An Introduction to the Homotopy Theory in Noncompact Spaces