Chaotic Maps, Fractals, and Rapid Fluctuations : With Applications to Chaotic Vibration of the Wave Equation (Synthesis Lectures on Mathematics & Statistics) （2ND）

Li, Liangliang/ Huang, Yu/ Chen, Goong

Springer International Publishing AG（2025/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 271 p.
• 商品コード 9783031848278

Full Description

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.