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.
