An introduction to chaotic dynamical systems.

*(English)*Zbl 0632.58005
Menlo Park, California, etc.: The Benjamin/Cummings Publishing Co., Inc. (Distr. by Addison-Wesley, Amsterdam). XIV, 320 p. (1986).

The book is an excellent introductory textbook on chaos in dynamical systems. It consists of three parts: one-dimensional dynamics, higher dimensional dynamics and complex analytic dynamics. In the first part all main ideas and concepts of modern dynamical systems theory along with important pure one-dimensional results are exposed and illustrated on the example of a one-dimensional quadratic map - structural stability, theory of bifurcations, Morse-Smale diffeomorphism, Sarkovskij theorem, homoclinic points, symbolic dynamics and kneading theory, period-doubling route to chaos etc.

The basic theme of the second part are dynamics of linear maps in \({\mathbb{R}}^ n\), horseshoe map, attractors, Anosov systems, Hopf bifurcation, Hénon map. In the last part polynomial maps of complex plane, their Julia sets, and the linearization of analytic map near an attracting fixed point are considered.

The book is written with great pedagogical skill and is accessible and interesting not only to students in mathematics but also researchers in other disciplines.

The basic theme of the second part are dynamics of linear maps in \({\mathbb{R}}^ n\), horseshoe map, attractors, Anosov systems, Hopf bifurcation, Hénon map. In the last part polynomial maps of complex plane, their Julia sets, and the linearization of analytic map near an attracting fixed point are considered.

The book is written with great pedagogical skill and is accessible and interesting not only to students in mathematics but also researchers in other disciplines.

Reviewer: E.D.Belokolos

##### MSC:

37-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory |

37Dxx | Dynamical systems with hyperbolic behavior |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

37G99 | Local and nonlocal bifurcation theory for dynamical systems |