Introduction to the Modern Theory of Dynamical Systems

Name: Introduction to the Modern Theory of Dynamical Systems
Price: 76.63 USD
Availability: InStock
ISBN: 9780521575577

ISBN-10: 0521575575

ISBN-13: 9780521575577

Edition: 1996

Authors: Anatole Katok, Boris Hasselblatt, B. Doran, P. Flajolet, M. Ismail

List price: $88.99

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Description:

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…

Book details

List price: $88.99
Copyright year: 1996
Publisher: Cambridge University Press
Publication date: 12/28/1996
Binding: Paperback
Pages: 824
Size: 6.26" wide x 9.25" long x 2.01" tall
Weight: 2.530
Language: English




Examples and Fundamental Concepts


Introduction



First examples



Equivalence, classification, and invariants



Principle classes of asymptotic invariants



Statistical behavior of the orbits and introduction to ergodic theory



Smooth invariant measures and more examples



Local Analysis and Orbit Growth



Local hyperbolic theory and its applications



Transversality and genericity



Orbit growth arising from topology



Variational aspects of dynamics



Low-Dimensional Phenomena



Introduction: What is low dimensional dynamics



Homeomorphisms of the circle



Circle diffeomorphisms



Twist maps



Flows on surfaces and related dynamical systems



Continuous maps of the interval



Smooth maps of the interval



Hyperbolic Dynamical Systems



Survey of examples



Topological properties of hyperbolic sets



Metric structure of hyperbolic sets



Equilibrium states and smooth invariant measures



Sopplement and Appendix



Dynamical systems with nonuniformly hyperbolic behavior