Chaotic Maps
eBook - PDF

Chaotic Maps

Dynamics, Fractals, and Rapid Fluctuations

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Chaotic Maps

Dynamics, Fractals, and Rapid Fluctuations

Book details
Table of contents
Citations

About This Book

This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a new viewpoint developed by the authors in recent years. Two appendices are also provided in order to ease the transitions for the readership from discrete-time dynamical systems to continuous-time dynamical systems, governed by ordinary and partial differential equations. Table of Contents: Simple Interval Maps and Their Iterations / Total Variations of Iterates of Maps / Ordering among Periods: The Sharkovski Theorem / Bifurcation Theorems for Maps / Homoclinicity. Lyapunoff Exponents / Symbolic Dynamics, Conjugacy and Shift Invariant Sets / The Smale Horseshoe / Fractals / Rapid Fluctuations of Chaotic Maps on RN / Infinite-dimensional Systems Induced by Continuous-Time Difference Equations

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Yes, you can access Chaotic Maps by Goong Chen,Yu Huang in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Springer
Year
2022
ISBN
9783031024030
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Cover
  2. Copyright Page
  3. Title Page
  4. Contents
  5. Preface
  6. Simple Interval Maps and Their Iterations
  7. Total Variations of Iterates of Maps
  8. Ordering among Periods: The Sharkovski Theorem
  9. Bifurcation Theorems for Maps
  10. Homoclinicity. Lyapunoff Exponents
  11. Symbolic Dynamics, Conjugacy and Shift Invariant Sets
  12. The Smale Horseshoe
  13. Fractals
  14. Rapid Fluctuations of Chaotic Maps on RN
  15. Infinite-dimensional Systems Induced by Continuous-Time Difference Equations
  16. Introduction to Continuous-Time Dynamical Systems
  17. Chaotic Vibration of the Wave Equation due to Energy Pumping and van der Pol Boundary Conditions
  18. Bibliography
  19. Authors' Biographies
  20. Index