Topological Dynamics Of Random Dynamical Systems

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Topological Dynamics Of Random Dynamical Systems

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Author : Nguyen Dinh Cong
language : en
Publisher: Oxford University Press
Release Date : 1997

Topological Dynamics Of Random Dynamical Systems written by Nguyen Dinh Cong and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

This book is the first systematic treatment of the theory of topological dynamics of random dynamical systems. A relatively new field, the theory of random dynamical systems unites and develops the classical deterministic theory of dynamical systems and probability theory, finding numerous applications in disciplines ranging from physics and biology to engineering, finance and economics. This book presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structural stability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory.

Random Dynamical Systems

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Author : Ludwig Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Random Dynamical Systems written by Ludwig Arnold 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 2013-04-17 with Mathematics categories.

Background and Scope of the Book This book continues, extends, and unites various developments in the intersection of probability theory and dynamical systems. I will briefly outline the background of the book, thus placing it in a systematic and historical context and tradition. Roughly speaking, a random dynamical system is a combination of a measure-preserving dynamical system in the sense of ergodic theory, (D,F,lP', (B(t))tE'lf), 'II'= JR+, IR, z+, Z, with a smooth (or topological) dy namical system, typically generated by a differential or difference equation :i: = f(x) or Xn+l = tp(x.,), to a random differential equation :i: = f(B(t)w,x) or random difference equation Xn+l = tp(B(n)w, Xn)· Both components have been very well investigated separately. However, a symbiosis of them leads to a new research program which has only partly been carried out. As we will see, it also leads to new problems which do not emerge if one only looks at ergodic theory and smooth or topological dynam ics separately. From a dynamical systems point of view this book just deals with those dynamical systems that have a measure-preserving dynamical system as a factor (or, the other way around, are extensions of such a factor). As there is an invariant measure on the factor, ergodic theory is always involved.

Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces

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Author : M. Bachir Bekka
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-11

Ergodic Theory And Topological Dynamics Of Group Actions On Homogeneous Spaces written by M. Bachir Bekka 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 2000-05-11 with Mathematics categories.

This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

Dynamical Systems And Random Processes

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Author : Jane Hawkins
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-23

Dynamical Systems And Random Processes written by Jane Hawkins 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 2019-09-23 with Mathematics categories.

This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13–15, 2018, at Agnes Scott College, Decatur, Georgia. The papers cover various topics in dynamics and randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages. The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.

Local Entropy Theory Of A Random Dynamical System

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Author : Anthony H. Dooley
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20

Local Entropy Theory Of A Random Dynamical System written by Anthony H. Dooley 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 2014-12-20 with Mathematics categories.

In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Handbook Of Dynamical Systems

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Author : A. Katok
language : en
Publisher: Elsevier
Release Date : 2005-12-17

Handbook Of Dynamical Systems written by A. Katok and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-17 with Mathematics categories.

This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).. Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.

Probability Towards 2000

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Author : L. Accardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Probability Towards 2000 written by L. Accardi 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.

Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.

An Introduction To Stochastic Dynamics

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Author : Jinqiao Duan
language : en
Publisher: Cambridge University Press
Release Date : 2015-04-13

An Introduction To Stochastic Dynamics written by Jinqiao Duan 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 2015-04-13 with Mathematics categories.

An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

Lyapunov Exponents And Invariant Manifolds For Random Dynamical Systems In A Banach Space

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Author : Zeng Lian
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Lyapunov Exponents And Invariant Manifolds For Random Dynamical Systems In A Banach Space written by Zeng Lian 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 2010 with Mathematics categories.

The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.

Random Dynamical Systems

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Author : Rabi Bhattacharya
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-08

Random Dynamical Systems written by Rabi Bhattacharya 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 2007-01-08 with Mathematics categories.

This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.