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Zbl 0632.58005
Devaney, Robert L.
An introduction to chaotic dynamical systems. (English)
[B] Menlo Park, California, etc.: The Benjamin/Cummings Publishing Co., Inc. (Distr. by Addison-Wesley, Amsterdam). XIV, 320 p. (1986). ISBN 0-8053-1601-9

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. \par The basic theme of the second part are dynamics of linear maps in ${\bbfR}\sp n$, 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. \par 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.
[E.D.Belokolos]

MSC 2000:: *37-01 Instructional exposition (Dynamical systems and ergodic theory)
37Dxx Dynamical systems with hyperbolic behavior
37D45 Strange attractors, chaotic dynamics
37G99 Bifurcation theory

Keywords: dynamical systems; one-dimensional quadratic map; structural stability; theory of bifurcations; Morse-Smale diffeomorphism; Sarkovskij theorem; homoclinic points; symbolic dynamics; kneading theory; period-doubling; chaos; horseshoe map; attractors; Anosov systems; Hopf bifurcation; Hénon map; Julia sets; attracting fixed point

Citations: Zbl 0695.58002

Cited in: Zbl 1196.92019 Zbl 1115.47008 Zbl 1166.37300 Zbl 1070.26004 Zbl 1025.37001 Zbl 0840.54031 Zbl 0912.54032 Zbl 0695.58002 Zbl 0676.54041 Zbl 0672.62001

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