Introduction to Chaotic Dynamical Systems

ISBN-10: 0813340853
ISBN-13: 9780813340852
Edition: 2nd 2003 (Revised)
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Description: Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and highlights current research in several areas.

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Book details

List price: $58.00
Edition: 2nd
Copyright year: 2003
Publisher: Westview Press
Publication date: 2/7/2003
Binding: Paperback
Pages: 362
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 1.012
Language: English

Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and highlights current research in several areas.

Preface
One-Dimensional Dynamics
Examples of dynamical systems
Preliminaries from calculus
Elementary definitions
Hyperbolicity
An example: the quadratic family
Symbolic dynamics
Topological conjugacy
Chaos
Structural stability
Sarkovskii's theorem
The Schwarzian derivative
Bifurcation theory
Another view of period three
Maps of the circle
Morse-Smale diffeomorphisms
Homoclinic points and bifurcations
The period-doubling route to chaos
The kneading theory
Genealogy of periodic points
Higher Dimensional Dynamics
Preliminaries from linear algebra and advanced calculus
The dynamics of linear maps: two and three dimensions
The horseshoe map
Hyperbolic toral automorphisms
Attractors
The stable and unstable manifold theorem
Global results and hyperbolic sets
The Hopf bifurcation
The Henon map
Complex Analytic Dynamics
Preliminaries from complex analysis
Quadratic maps revisited
Normal families and exceptional points
Periodic points
The Julia set
The geometry of Julia sets
Neutral periodic points
The Mandelbrot set
An example: the exponential function
Color Plates
Index

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