Introduction to the Modern Theory of Dynamical Systems available in Hardcover
- Pub. Date:
- Cambridge University Press
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.
|Publisher:||Cambridge University Press|
|Series:||Encyclopedia of Mathematics and its Applications Series , #54|
|Product dimensions:||6.14(w) x 9.21(h) x 1.69(d)|
Table of ContentsPart 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.