000			02090cam a2200277 i 4500
001			137966
003			ISI Library, Kolkata
005			20171012122811.0
008			160322s2016 riua b 001 0 eng
020			_a9781470427993 (hbk. : acidfree paper)
040			_aISI Library
082	0	4	_a515.39 _223 _bW467
100	1		_aWen, Lan, _eauthor
245	1	0	_aDifferentiable dynamical systems : _ban introduction to structural stability and hyperbolicity / _cLan Wen.
260			_aProvidence : _bAmerican Mathematical Society, _c©2016.
300			_axi, 192 pages : _billustrations ; _c26 cm.
490	0		_aGraduate studies in mathematics ; _v173.
504			_aIncludes bibliographical references and index.
505	0		_a1. Basics of dynamical systems -- 2. Hyperbolic fixed points -- 3. Horseshoes, toral automorphisms, and solenoids -- 4. Hyperbolic sets -- 5. Axiom A, no-cycle condition, and Ω-stability -- 6. Quasi-hyperbolicity and linear transversality -- Bibliography -- Index.
520			_aThis is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale.While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study.
650		0	_aDifferential equations.
650		0	_aNonlinear differential equations.
650		0	_aDynamics.
650		0	_aExponential functions.
942			_2ddc _cBK
999			_c424022 _d424022