Applied Mathematical Sciences

Stochastic Aspects of Dynamics

By: Andrzej Lasota, Michael C. Mackey

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Hardcover | 1 April 1998 | Edition Number 2

At a Glance

Hardcover
492 Pages

Edition Type
Revised

Dimensions(cm)
23.39 x 15.6 x 2.69

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In recent years there has been an explosive growth in the study of physical, biological, and economic systems that can be profitably studied using densities. Because of the general inaccessibility of the mathematical literature to the nonspecialist, little diffusion of the applicable mathematics into the study of these "chaotic" systems has taken place. This book will help bridge that gap.
To show how densities arise in simple deterministic systems, the authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from many fields to illustrate the utility of the concepts and techniques presented, and the ideas in this book should thus prove useful in the study of a number of applied sciences.
The authors assume that the reader has a knowledge of advanced calculus and differential equations. Basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed. Physicists, chemists, and biomathematicians studying chaotic behavior will find this book of value. It will also be a useful reference or text for mathematicians and graduate students working in ergodic theory and dynamical systems.

Industry Reviews

"This is a truly outstanding book. It is so well and carefully written that, despite the complexity of the subject matte and the difficulty of some of the mathematics, virtually everything is completely clear on a first reading. Indeed, the book is much more absorbing than most novels." Probability in the Engineering + Informational Sciences

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Chaos Theory Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory Probability & Statistics Geometry Fractal Geometry Calculus & Mathematical Analysis

Differential Calculus & Equations Science Science in General Physics Mathematical Physics

Preface to the Second Edition
Preface to the First Edition
Introduction	p. 1
The Toolbox	p. 17
Markov and Frobenius-Perron Operators	p. 37
Studying Chaos with Densities	p. 51
The Asymptotic Properties of Densities	p. 85
The Behavior of Transformations on Intervals and Manifolds	p. 139
Continuous Time Systems: An Introduction	p. 189
Discrete Time Processes Embedded in Continuous Time Systems	p. 251
Entropy	p. 283
Stochastic Perturbation of Discrete Time Systems	p. 303
Stochastic Perturbation of Continuous Time Systems	p. 335
Markov and Foias Operators	p. 393
References	p. 449
Notation and Symbols	p. 457
Index	p. 461
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Mathematical Sciences

Stochastic Aspects of Dynamics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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