Introduction to the Modern Theory of Dynamical Systems
Introduction to the Modern Theory of Dynamical Systems
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.
- Over 400 exercises, with solution hints
- Comprehensive - goes from elementary theory to recent research
- Katok is one of the world's leading researchers in dynamical systems
Reviews & endorsements
"...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
Product details
December 1996Paperback
9780521575577
824 pages
235 × 159 × 51 mm
1.16kg
Available
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.
