Chaotic Maps, Fractals, and Rapid Fluctuations: With Applications to Chaotic Vibration of the Wave Equation (Second Edition 2025) (Synthesis Lectures on Mathematics & Statistics)

By: Yu Huang and Goong Chen and Liangliang Li

Sign Up Now! Already a Member? Log In
You must be logged into Bookshare to access this title. Learn about membership options, or view our freely available titles.

Synopsis: This book was developed from lecture notes for an introductory graduate course and provides an essential introduction to chaotic maps in finite-dimensional spaces. Furthermore, the authors show how to apply this theory to infinite-dimensional systems corresponding to partial differential equations to study chaotic vibration of the wave equation subject to various types of nonlinear boundary conditions. The book provides background on chaos as a highly interesting nonlinear phenomenon and explains why it is one of the most important scientific findings of the past three decades. In addition, the book covers key topics including one-dimensional dynamical systems, bifurcations, general topological, symbolic dynamical systems, and fractals. The authors also show a class of infinite-dimensional nonlinear dynamical systems, which are reducible to interval maps, plus rapid fluctuations of chaotic maps. This second edition includes updated and expanded chapters as well as additional problems.