Introduction to the Modern Theory of Dynamical Systems

by Anatole Katok, Boris Hasselblatt

Overview

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.

Product Details

ISBN-13:	9780521341875
Publisher:	Cambridge University Press
Publication date:	04/28/1995
Series:	Encyclopedia of Mathematics and its Applications Series , #54
Pages:	824
Product dimensions:	6.14(w) x 9.21(h) x 1.69(d)

Table of Contents

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 dimensional dynamics; 11. Homeomorphisms of the circle; 12. Circle diffeomorphisms; 13. Twist maps; 14. Flows on surfaces and related dynamical systems; 15. Continuous maps of the interval; 16. Smooth maps of the interval; Part IV. Hyperbolic Dynamical Systems; 17. Survey of examples; 18. Topological properties of hyperbolic sets; 19. Metric structure of hyperbolic sets; 20. Equilibrium states and smooth invariant measures; Part V. Sopplement and Appendix; 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.

Editorial Reviews

"...well written and clear...a valuable reference for engineers and mechanicians." H.W. Haslach Jr., Applied Mechanics Reviews

"The book is a pleasure to read." Edoh Amiran, Mathematical Reviews

"The notes section at the end of the book is complete and quite helpful. There are hints and answers provided for a good percentage of the problems in the book. The problems range from fairly straightforward ones to results that I remember reading in research papers over the last 10-20 years....I recommend the text as an exceptional reference..." Richard Swanson, SIAM Review

From the Publisher