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Dynamical Systems - An Introduction (Paperback, 2013 ed.)
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Dynamical Systems - An Introduction (Paperback, 2013 ed.)
Series: Universitext
Expected to ship within 10 - 15 working days
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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 Poincare-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, Poincare'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.
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