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Introduction to the modern theory of dynamical systems

Author: Anatole B Katok; Boris Hasselblatt
Publisher: Cambridge, England ; New York : Cambridge University Press, ©1995.
Series: Encyclopedia of mathematics and its applications, v. 54.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with all main areas of mathematics. The authors  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Anatole B Katok; Boris Hasselblatt
ISBN: 0521575575 9780521575577 0521341876 9780521341875
OCLC Number: 318267575
Notes: Reimpresión de 1999.
Description: xviii, 802 p. : il. ; 24 cm.
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.
Series Title: Encyclopedia of mathematics and its applications, v. 54.
Responsibility: Anatole Katok, Boris Hasselblatt ; with a supplement by Anatole Katok and Leonardo Mendoza.
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' ... there is no other treatment coming close in terms of comprehensiveness and readability ... it is indispensable for anybody working on dynamical systems in almost any context, and even experts Read more...

 
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