Discrete Dynamical Systems
by Arild Wikan
Publisher: Bookboon 2013
Number of pages: 254
This book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential in order to understand the fascinating behavior of nonlinear discrete dynamical systems. The theory is illuminated by several examples and exercises, many of them taken from population dynamical studies. Solution methods of linear systems as well as solution methods of discrete optimization (control) problems are also included.
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These notes describe several situations in dynamics where the notion of valuations on rings provides a simple language in which to describe and exploit hyperbolicity. This approach goes a little beyond simply providing a convenient language.
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Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics.
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