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＜E-Book＞
Dynamical Systems : An Introduction / by Luis Barreira, Claudia Valls
(Universitext. ISSN:21916675)

Edition	1st ed. 2013.
Publisher	(London : Springer London : Imprint: Springer)
Year	2013
Language	English
Size	IX, 209 p. 44 illus : online resource
Authors	*Barreira, Luis author Valls, Claudia author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Differential equations LCSH:Geometry, Hyperbolic FREE:Dynamical Systems FREE:Global Analysis and Analysis on Manifolds FREE:Differential Equations FREE:Hyperbolic Geometry
Notes	Introduction -- Basic Notions and Examples -- Topological Dynamics -- Low-Dimensional Dynamics -- Hyperbolic Dynamics I -- Hyperbolic Dynamics II -- Symbolic Dynamics -- Ergodic Theory The 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 HTTP:URL=https://doi.org/10.1007/978-1-4471-4835-7

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