Invariant Manifolds Entropy And Billiards Smooth Maps With Singularities
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Invariant Manifolds Entropy And Billiards Smooth Maps With Singularities
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Author : Anatole Katok
language : en
Publisher: Springer
Release Date : 2006-12-08
Invariant Manifolds Entropy And Billiards Smooth Maps With Singularities written by Anatole Katok and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Lecture Notes In Mathematics
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Author :
language : en
Publisher:
Release Date : 1964
Lecture Notes In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Differentiable dynamical systems categories.
Invariant Manifolds Entropy And Billiards Smooth Maps With Singularities
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Author : Anatole Katok
language : en
Publisher:
Release Date : 2014-01-15
Invariant Manifolds Entropy And Billiards Smooth Maps With Singularities written by Anatole Katok and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Dynamics Reported
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Dynamics Reported written by 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.
DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dy namical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed exposition of ideas, restriction to typical results - rather than the most general one- and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents The "Spectral" Decomposition for One-Dimensional Maps Alexander M. Blokh Introduction and Main Results 1. 1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 0. 1. 1. Historical Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 2. A Short Description of the Approach Presented . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 3. Solenoidal Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Basic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 4.
Ergodic Theory Open Dynamics And Coherent Structures
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Author : Wael Bahsoun
language : en
Publisher: Springer Science & Business
Release Date : 2014-05-02
Ergodic Theory Open Dynamics And Coherent Structures written by Wael Bahsoun and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-02 with Mathematics categories.
This book is comprised of selected research articles developed from a workshop on Ergodic Theory, Probabilistic Methods and Applications, held in April 2012 at the Banff International Research Station. It contains contributions from world leading experts in ergodic theory, numerical dynamical systems, molecular dynamics and ocean/atmosphere dynamics, nonequilibrium statistical mechanics. The volume will serve as a valuable reference for mathematicians, physicists, engineers, biologists and climate scientists, who currently use, or wish to learn how to use, probabilistic techniques to cope with dynamical models that display open or non-equilibrium behavior.
Smooth Ergodic Theory For Endomorphisms
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Author : Min Qian
language : en
Publisher: Springer
Release Date : 2009-07-07
Smooth Ergodic Theory For Endomorphisms written by Min Qian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-07 with Mathematics categories.
Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms. Its focus is on the relations between entropy, Lyapunov exponents and dimensions.
Chaotic Billiards
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Author : Nikolai Chernov
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-18
Chaotic Billiards written by Nikolai Chernov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-18 with Mathematics categories.
This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.
Geometry Of The Generalized Geodesic Flow And Inverse Spectral Problems
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Author : Vesselin M. Petkov
language : en
Publisher: John Wiley & Sons
Release Date : 2017-01-30
Geometry Of The Generalized Geodesic Flow And Inverse Spectral Problems written by Vesselin M. Petkov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-30 with Mathematics categories.
This book is a new edition of a title originally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson summation formula and the related study of singularities. This book presents these in a closed and comprehensive form, and the exposition is based on a combination of different tools and results from dynamical systems, microlocal analysis, spectral and scattering theory. The content of the first edition is still relevant, however the new edition will include several new results established after 1992; new text will comprise about a third of the content of the new edition. The main chapters in the first edition in combination with the new chapters will provide a better and more comprehensive presentation of importance for the applications inverse results. These results are obtained by modern mathematical techniques which will be presented together in order to give the readers the opportunity to completely understand them. Moreover, some basic generic properties established by the authors after the publication of the first edition establishing the wide range of applicability of the Poison relation will be presented for first time in the new edition of the book.
Introduction To Smooth Ergodic Theory
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Author : Luís Barreira
language : en
Publisher: American Mathematical Society
Release Date : 2023-05-19
Introduction To Smooth Ergodic Theory written by Luís Barreira and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-19 with Mathematics categories.
This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.
Ergodic Theory
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Author : Cesar E. Silva
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Ergodic Theory written by Cesar E. Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras