Introduction To Topological Dynamical Systems Ii

Introduction to Topological Dynamical Systems II

Dynamical Systems II

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. Then the ergodic theory of smooth dynamical systems is presented - hyperbolic theory, billiards, one-dimensional systems and the elements of KAM theory. Numerous examples are presented carefully along with the ideas underlying the most important results. The last part of the book deals with the dynamical systems of statistical mechanics, and in particular with various kinetic equations. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.

Topological Dynamical Systems

There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.