This book presents the study of ergodic properties of so-called chaotic dynamical systems. One of the central topics is the interplay between deterministic and quasi-stochastic behavior in chaotic dynamics and between properties of continuous dynamical systems and those of their discrete approximations. Using simple examples, the author describes the main phenomena known in chaotic dynamical systems, studying topics such as the operator approach in chaotic dynamics, stochastic stability, and the so-called coupled systems. The last two chapters are devoted to problems of numerical modelling of chaotic dynamics.

Readership

Graduate students and research mathematicians interested in ergodic theory, dynamical systems, and applications.

Table of Contents

• Introduction (Chapter 1)
• Operator approach in chaotic dynamics (Chapter 2)
• Random perturbations of dynamical systems (Chapter 3)
• Weakly coupled dynamical systems (Chapter 4)
• Phase space discretization in dyanmical systems (Chapter 5)
• Ergodic properties of some methods for numerical modeling of chaotic dynamics (Chapter 6)
• References
• Index