Dynamical Systems Ergodic Theory And Applications
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Dynamical Systems Ergodic Theory And Applications
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Author : L.A. Bunimovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-04-05
Dynamical Systems Ergodic Theory And Applications written by L.A. Bunimovich 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 2000-04-05 with Mathematics categories.
This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.
Dynamical Systems Ii
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Author : Ya.G. Sinai
language : en
Publisher: Springer
Release Date : 1996-12-01
Dynamical Systems Ii written by Ya.G. Sinai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-01 with Mathematics categories.
Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. Then the ergodic theory of smooth dynamical systems is presented - hyperbolic theory, billiards, one-dimensional systems and the elements of KAM theory. Numerous examples are presented carefully along with the ideas underlying the most important results. The last part of the book deals with the dynamical systems of statistical mechanics, and in particular with various kinetic equations. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.
Dynamical Systems Ergodic Theory With Applications To Dynamical Systems And Statistical Mechanics
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Author :
language : en
Publisher:
Release Date : 1988
Dynamical Systems Ergodic Theory With Applications To Dynamical Systems And Statistical Mechanics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Celestial mechanics categories.
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers 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 2011-10-05 with Mathematics categories.
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Dynamical Systems Ergodic Theory With Applications To Dynamical Systems And Statistical Mechanics
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Author :
language : en
Publisher:
Release Date : 1987
Dynamical Systems Ergodic Theory With Applications To Dynamical Systems And Statistical Mechanics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Celestial mechanics categories.
Ergodic Dynamics
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Author : Jane Hawkins
language : en
Publisher: Springer Nature
Release Date : 2021-01-28
Ergodic Dynamics written by Jane Hawkins and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-28 with Mathematics categories.
This textbook provides a broad introduction to the fields of dynamical systems and ergodic theory. Motivated by examples throughout, the author offers readers an approachable entry-point to the dynamics of ergodic systems. Modern and classical applications complement the theory on topics ranging from financial fraud to virus dynamics, offering numerous avenues for further inquiry. Starting with several simple examples of dynamical systems, the book begins by establishing the basics of measurable dynamical systems, attractors, and the ergodic theorems. From here, chapters are modular and can be selected according to interest. Highlights include the Perron–Frobenius theorem, which is presented with proof and applications that include Google PageRank. An in-depth exploration of invariant measures includes ratio sets and type III measurable dynamical systems using the von Neumann factor classification. Topological and measure theoretic entropy are illustrated and compared in detail, with an algorithmic application of entropy used to study the papillomavirus genome. A chapter on complex dynamics introduces Julia sets and proves their ergodicity for certain maps. Cellular automata are explored as a series of case studies in one and two dimensions, including Conway’s Game of Life and latent infections of HIV. Other chapters discuss mixing properties, shift spaces, and toral automorphisms. Ergodic Dynamics unifies topics across ergodic theory, topological dynamics, complex dynamics, and dynamical systems, offering an accessible introduction to the area. Readers across pure and applied mathematics will appreciate the rich illustration of the theory through examples, real-world connections, and vivid color graphics. A solid grounding in measure theory, topology, and complex analysis is assumed; appendices provide a brief review of the essentials from measure theory, functional analysis, and probability.
Ergodic Theory With Applications To Dynamical Systems And Statistical Mechanics
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Author : I︠A︡kov Grigorʹevich Sinaĭ
language : en
Publisher: Springer
Release Date : 1989
Ergodic Theory With Applications To Dynamical Systems And Statistical Mechanics written by I︠A︡kov Grigorʹevich Sinaĭ and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
1. Ordinary differential equations and smooth dynamical systems by D.V. Anosov, V.I. Arnold (eds.). 2. Ergodic theory with applications to dynamical systems an d statistical mechanics by Ya. G. Sinai (ed.). 3. [without special title]. 4. S ymplectic geometry and its applications by V.I. Arnold, S.P. Novikov (eds.).
Dynamical Systems Ii
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Author : Ya G. Sinai
language : en
Publisher:
Release Date : 2014-01-15
Dynamical Systems Ii written by Ya G. Sinai 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.
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems
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Author : Bernold Fiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems written by Bernold Fiedler 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 2001 with Mathematics categories.
This book summarizes and highlights progress in Dynamical Systems achieved during six years of the German Priority Research Program "Ergotic Theory, Analysis, and Efficient Simulation of Dynamical Systems", funded by the Deutsche Forschungsgemeinschaft (DFG). The three fundamental topics of large time behavior, dimension, and measure are tackled with by a rich circle of uncompromisingly rigorous mathematical concepts. The range of applied issues comprises such diverse areas as crystallization and dendrite growth, the dynamo effect, efficient simulation of biomolecules, fluid dynamics and reacting flows, mechanical problems involving friction, population biology, the spread of infectious diseases, and quantum chaos. The surveys in the book are addressed to experts and non-experts in the mathematical community alike. In addition they intend to convey the significance of the results for applications fair into the neighboring disciplines of Science.
Dynamical Systems And Ergodic Theory
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Author : Mark Pollicott
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29
Dynamical Systems And Ergodic Theory written by Mark Pollicott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).