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008			090210s1995 enka |b 001 0 eng d
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050	0	0	_aQA614.8 _b.K38 1995
100	1		_aKatok, A. B. _949723
245	1	0	_aIntroduction to the modern theory of dynamical systems / _cAnatole Katok, Boris Hasselblatt ; with a supplement by Anatole Katok and Leonardo Mendoza.
260			_aCambridge ; _aNew York, NY, USA : _bCambridge University Press, _c1995.
300			_axviii, 802 p. : _bill. ; _c24 cm.
440		0	_aEncyclopedia of mathematics and its applications ; _949724
505			_aPart 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.
520			_aThis 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 orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. 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.
650		0	_aDifferentiable dynamical systems. _925098
942			_2lcc _n0 _cBK
999			_c23607 _d23607