An introduction to chaotic dynamical systems
著者
書誌事項
An introduction to chaotic dynamical systems
CRC Press, 2022
3rd ed
- : hbk
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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
「Nielsen BookData」 より
