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Catalogue Information
Field name	Details
Dewey Class	515.39
Dewey Class	515.48
Title	Dynamical Systems ([Ebook]) : An Introduction / by Luis Barreira, Claudia Valls.
Author	Barreira, Luis
Added Personal Name	Valls, Claudia
Other name(s)	SpringerLink (Online service)
Publication	London : Springer
Publication	, 2013.
Physical Details	IX, 209 pages : 44 illus. : online resource.
Series	Universitext 0172-5939
ISBN	9781447148357
Summary Note	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 PoincarÃ©-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, PoincarÃ©'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.:
Contents note	Introduction -- Basic Notions and Examples -- Topological Dynamics -- Low-Dimensional Dynamics -- Hyperbolic Dynamics I -- Hyperbolic Dynamics II -- Symbolic Dynamics -- Ergodic Theory.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4471-4835-7
Links to Related Works	Subject References: Differentiable dynamical systems . Differential equation . Dynamical systems and ergodic theory . Global analysis . Global Analysis and Analysis on Manifolds . Hyperbolic Geometry . Mathematics . Ordinary differential equations . Authors: author . Barreira, Luis . Valls, Claudia . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 515.39 . 515.48 . 515.39 (DDC 23) .

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Dynamical Systems: An Introduction

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