An introduction to chaotic dynamical systems

書誌事項

An introduction to chaotic dynamical systems

Robert L. Devaney

CRC Press, 2022

3rd ed

  • : hbk

大学図書館所蔵 件 / 12

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注記

Includes bibliographical references (p. 413-416) and index

内容説明・目次

内容説明

* Greatly expanded coverage complex dynamics now in Chapter 2 * The third chapter is now devoted to higher dimensional dynamical systems. * Chapters 2 and 3 are independent of one another. * New exercises have been added throughout.

目次

I One Dimensional Dynamics 1.A Visual and Historical Tour 2.Examples of Dynamical Systems 3.Elementary Definitions 4.Hyperbolicity 5.An Example: The Logistic Family 6.Symbolic Dynamics 7.Topological Conjugacy 8.Chaos 9.Structural Stability 10.Sharkovsky's Theorem 11.The Schwarzian Derivative 12.Bifurcations 13.Another View of Period Three 14.Period-Doubling Route to Chaos 15.Homoclinic Points and Bifurcations 16.Maps of the Circle 17.Morse-Smale Diffeomorphisms II Complex Dynamics 18.Quadratic Maps Revisited 19.Normal Families and Exceptional Points 20.Periodic Points 21.Properties of the Julia Set 22.The Geometry of the Julia Sets 23.Neutral Periodic Points 24.The Mandelbrot Set 25.Rational Maps 26.The Exponential Family III Higher Dimensional Dynamics 27.Dynamics of Linear Maps 28.The Smale Horseshoe Map 29.Hyperbolic Toral Automorphisms 30.Attractors 31.The Stable and Unstable Manifold Theorem 32.Global Results and Hyperbolic Maps 33.The Hopf Bifurcation 34.The Herron Map Appendix: Mathematical Preliminaries

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