Robert Devaney

An Introduction To Chaotic Dynamical Systems (eBook, PDF)

• Format: PDF

Produktbeschreibung

Robert L. Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 360
• Erscheinungstermin: 9. März 2018
• Englisch
• ISBN-13: 9780429970856
• Artikelnr.: 54084700

Autorenporträt

Robert Devaney

Inhaltsangabe

Part One: One-Dimensional Dynamics
Examples of Dynamical Systems
Preliminaries from Calculus
Elementary Definitions
Hyperbolicity
An example: the quadratic family
An Example: the Quadratic Family
Symbolic Dynamics
Topological Conjugacy
Chaos
Structural Stability
Sarlovskiis 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 Kneeding Theory
Geneaology of Periodic Units Part Two: 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
Hyperbolicm Toral Automorphisms
Attractors
The Stable and Unstable Manifold Theorem
Global Results and Hyperbolic Sets
The Hopf Bifurcation
The Hnon Map Part Three: 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