000			03375nam a22005175i 4500
001			978-1-4471-4835-7
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005			20140220082807.0
007			cr nn 008mamaa
008			121205s2013 xxk| s |||| 0|eng d
020			_a9781447148357 _9978-1-4471-4835-7
024	7		_a10.1007/978-1-4471-4835-7 _2doi
050		4	_aQA313
072		7	_aPBWR _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.39 _223
082	0	4	_a515.48 _223
100	1		_aBarreira, Luis. _eauthor.
245	1	0	_aDynamical Systems _h[electronic resource] : _bAn Introduction / _cby Luis Barreira, Claudia Valls.
264		1	_aLondon : _bSpringer London : _bImprint: Springer, _c2013.
300			_aIX, 209 p. 44 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_aIntroduction -- Basic Notions and Examples -- Topological Dynamics -- Low-Dimensional Dynamics -- Hyperbolic Dynamics I -- Hyperbolic Dynamics II -- Symbolic Dynamics -- Ergodic Theory.
520			_aThe theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.
650		0	_aMathematics.
650		0	_aDifferentiable dynamical systems.
650		0	_aGlobal analysis.
650		0	_aDifferential Equations.
650	1	4	_aMathematics.
650	2	4	_aDynamical Systems and Ergodic Theory.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
650	2	4	_aOrdinary Differential Equations.
650	2	4	_aHyperbolic Geometry.
700	1		_aValls, Claudia. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781447148340
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4471-4835-7
912			_aZDB-2-SMA
999			_c94710 _d94710