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.
"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
|Preface to the Second Edition|
|Preface to the First Edition|
|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|
|Stochastic Perturbation of Discrete Time Systems||p. 303|
|Stochastic Perturbation of Continuous Time Systems||p. 335|
|Markov and Foias Operators||p. 393|
|Notation and Symbols||p. 457|
|Table of Contents provided by Blackwell. All Rights Reserved.|
Series: Applied Mathematical Sciences
Number Of Pages: 474
Published: 1st April 1998
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5 x 2.54
Weight (kg): 0.88
Edition Number: 2
Edition Type: Revised