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<p class="MsoNormal">This book was developed from lecture notes for an introductory graduate course and provides an essential introduction to&#xa0;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.<span style="mso-spacerun: yes;">&#xa0; </span>The&#xa0;book provides background on&#xa0;chaos as a highly interesting nonlinear phenomenon and explains why it is one of the&#xa0; most important scientific findings of&#xa0;the&#xa0;past three decades. <span style="mso-spacerun: yes;">&#xa0;</span>In addition, the&#xa0;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.</p>

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Chaotic Maps, Fractals, and Rapid Fluctuations

  • 教材

  • 发表日期：

    2025年

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  • Liangliang Li,
  • Yu Huang,
  • Goong Chen

摘要

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.