Boris Hasselblatt, Anatole Katok

Introduction to the Modern Theory of Dynamical Systems

Herausgeber: Kotok, Anatole

• Gebundenes Buch

Produktbeschreibung

This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental 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 orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 824
• Erscheinungstermin: 9. Februar 2011
• Englisch
• Abmessung: 240mm x 161mm x 48mm
• Gewicht: 1387g
• ISBN-13: 9780521341875
• ISBN-10: 0521341876
• Artikelnr.: 20987551

Inhaltsangabe

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.