Introduction to the Modern Theory of Dynamical Systems [Paperback]

A self-contained comprehensive introduction to the mathematical theory of dynamical systems for students and researchers in mathematics, science and engineering.Beginning with a discussion of several elementary but crucial examples, this study provides a self-contained comprehensive exposition of the theory of dynamical systems. It is aimed at students and researchers in mathematics at all levels from advanced undergraduate and up.Beginning with a discussion of several elementary but crucial examples, this study provides a self-contained comprehensive exposition of the theory of dynamical systems. It is aimed at students and researchers in mathematics at all levels from advanced undergraduate and up.This book provides a self-contained comprehensive exposition of the theory of dynamical systems. The book begins with a discussion of several elementary but crucial examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate and up.Part I. Examples and Fundamental Concepts; Introduction; 1. First examples; 2. Equivalence, classification, and invariants; 3. Principle classes of asymptotic invariants; 4. Statistical behavior of the orbits and introduction to ergodic theory; 5. Smooth invariant measures and more examples; Part II. Local Analysis and Orbit Growth; 6. Local hyperbolic theory and its applications; 7. Transversality and genericity; 8. Orbit growth arising from topology; 9. Variational aspects of dynamics; Part III. Low-Dimensional Phenomena; 10. Introduction: What is low dimenlC&