Differentiable Dynamical Systems
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Differentiable Dynamical Systems
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Author : Lan Wen
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-07-20
Differentiable Dynamical Systems written by Lan Wen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-20 with Mathematics categories.
This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.
Qualitative Theory Of Differentiable Dynamical Systems
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Author : Shantao Liao
language : en
Publisher: Science Press New York
Release Date : 1996
Qualitative Theory Of Differentiable Dynamical Systems written by Shantao Liao and has been published by Science Press New York this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Medical categories.
Differential Equations And Dynamical Systems
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Author : Antonio Galves
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Differential Equations And Dynamical Systems written by Antonio Galves and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This volume contains contributed papers authored by participants of a Conference on Differential Equations and Dynamical Systems which was held at the Instituto Superior Tecnico (Lisbon, Portugal). The conference brought together a large number of specialists in the area of differential equations and dynamical systems and provided an opportunity to celebrate Professor Waldyr Oliva's 70th birthday, honoring his fundamental contributions to the field. The volume constitutes anoverview of the current research over a wide range of topics, extending from qualitative theory for (ordinary, partial or functional) differential equations to hyperbolic dynamics and ergodic theory.
Differentiable Dynamical Systems
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Author : Stephen Smale
language : en
Publisher:
Release Date : 1968
Differentiable Dynamical Systems written by Stephen Smale and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Differential topology categories.
Dynamical Systems
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Author : C.M. Place
language : en
Publisher: Routledge
Release Date : 2017-11-22
Dynamical Systems written by C.M. Place and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams) to develop the material, including a treatment of chaotic behavior. The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations. Applications in physics, engineering, and geology are considered and introductions to fractal imaging and cellular automata are given.
Handbook Of Dynamical Systems
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Author : H. Broer
language : en
Publisher: Elsevier
Release Date : 2010-11-10
Handbook Of Dynamical Systems written by H. Broer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
Differential Dynamical Systems Revised Edition
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Author : James D. Meiss
language : en
Publisher: SIAM
Release Date : 2017-01-24
Differential Dynamical Systems Revised Edition written by James D. Meiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.
Ergodic Theory And Differentiable Dynamics
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Author : Ricardo Mane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ergodic Theory And Differentiable Dynamics written by Ricardo Mane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.
Lectures In Differentiable Dynamics
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Author : Lawrence Markus
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
Lectures In Differentiable Dynamics written by Lawrence Markus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Offers an exposition of the central results of Differentiable Dynamics. This edition includes an Appendix reviewing the developments under five basic areas: nonlinear oscillations, diffeomorphisms and foliations, general theory; dissipative dynamics, general theory; conservative dynamics, and, chaos, catastrophe, and multi-valued trajectories.
Differentiable Dynamics
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Author : Zbigniew Nitecki
language : en
Publisher: Mit Press
Release Date : 1971
Differentiable Dynamics written by Zbigniew Nitecki and has been published by Mit Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
The subject of differentiable dynamical systems in the form recently developed by the group of mathematicians associated with S. Smale and M. Peixoto in the United States and with Ja. Sinai and D. Asonov in the Soviet Union is evoking great interest among this generation's mathematicians. Specialists teaching courses in this field as well as nonexperts interested in a comprehensive introduction should welcome Differentiable Dynamics,the first work to collect and explain in detail a wide selection of results and techniques which have formerly been scattered in the primary literature. Approaching this literature directly can, moreover, be somewhat treacherous since a number of obsolete results are embedded within it. In this regard, it is worth noting that one expert in this area who examined the book in manuscript wrote, "Nitecki has it seems to me made an admirable choice of material-both in what he has put in and what he has left out." Some of this material is so recent that at present it exists only in preprint form. The book has already proved itself from the standpoint of text use; it derives from a set of lecture notes prepared by the author for a graduate course in dynamical systems he conducted at Yale. Beyond the seminar room, mathematicians generally working in the area of topology and global analysis should find it a useful reference for the recent work in dynamics on manifolds. The book begins with an introduction to the Smale program and philosophy and goes on to give a detailed account of the subject, developing it from the simple case of the circle since all the topological complications of higher dimensions are absent but all the essential features of the subject are clearly visible. With this preparation, the student is able to proceed to the inherently difficult "horseshoe example" and its relation to symbolic dynamics. Differentiable Dynamicsconsists of the following chapters: Introduction: Flows and Diffeomorphisms-Preliminaries-The Circle-Periodic Points-Anosov Diffeomorphisms-The Horseshoe-Hyperbolic Sets-The -Stability Theorem-A Survey of Recent Work.