Topological Dynamics Of Random Dynamical Systems PDF Download
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| Author | : Nguyen Dinh Cong |
| Publisher | : Oxford University Press |
| Total Pages | : 216 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780198501572 |
Download Topological Dynamics of Random Dynamical Systems Book in PDF, ePub and Kindle
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.
| Author | : Ludwig Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 590 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662128780 |
Download Random Dynamical Systems Book in PDF, ePub and Kindle
The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
| Author | : Anthony H. Dooley |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 118 |
| Release | : 2014-12-20 |
| Genre | : Mathematics |
| ISBN | : 1470410559 |
Download Local Entropy Theory of a Random Dynamical System Book in PDF, ePub and Kindle
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.
| Author | : Ethan Akin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 273 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : 0821849328 |
Download The General Topology of Dynamical Systems Book in PDF, ePub and Kindle
Recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results. This book collects these results, both old and new, and organises them into a natural foundation for all aspects of dynamical systems theory.
| Author | : N. Aoki |
| Publisher | : Elsevier |
| Total Pages | : 425 |
| Release | : 1994-06-03 |
| Genre | : Mathematics |
| ISBN | : 008088721X |
Download Topological Theory of Dynamical Systems Book in PDF, ePub and Kindle
This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.
| Author | : |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 277 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642612156 |
Download Dynamics Reported Book in PDF, ePub and Kindle
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.
| Author | : Rabindra Nath Bhattacharya |
| Publisher | : |
| Total Pages | : 463 |
| Release | : 2007 |
| Genre | : Random dynamical systems |
| ISBN | : 9780511274367 |
Download Random Dynamical Systems Book in PDF, ePub and Kindle
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.
| Author | : Jane Hawkins |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 265 |
| Release | : 2019-09-23 |
| Genre | : Differentiable dynamical systems |
| ISBN | : 1470448319 |
Download Dynamical Systems and Random Processes Book in PDF, ePub and Kindle
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.
| Author | : Hans Crauel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 457 |
| Release | : 1999-03-26 |
| Genre | : Mathematics |
| ISBN | : 0387985123 |
Download Stochastic Dynamics Book in PDF, ePub and Kindle
Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.
| Author | : Bernold Fiedler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 816 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642565891 |
Download Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems Book in PDF, ePub and Kindle
Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
