Global bifurcations and chaos : analytical methods /

Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms which give rise to chaos (i.e., homoclinic and heteroclinic motions) and derives explicit techniques where...

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Bibliographic Details
Main Author:	Wiggins, Stephen
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	New York : Springer-Verlag, [1988]
Series:	Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 73.
Subjects:	Bifurcation theory. Chaotic behavior in systems. Differential equations > Numerical solutions. Bifurcation, Théorie de la. Équations différentielles > Solutions numériques. Chaos. Niet-lineaire dynamica. Bifurcatie. Comportement chaotique des systèmes. Equations différencielles > Solutions numériques. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

1. Introduction: Background for Ordinary Differential Equations and Dynamical Systems
1.1. The Structure of Solutions of Ordinary Differential Equations
1.2. Conjugacies
1.3. Invariant Manifolds
1.4. Transversality, Structural Stability, and Genericity
1.5. Bifurcations
1.6. Poincar Maps
2. Chaos: Its Descriptions and Conditions for Existence
2.1. The Smale Horseshoe
2.2. Symbolic Dynamics
2.3. Criteria for Chaos: The Hyperbolic Case
2.4. Criteria for Chaos: The Nonhyperbolic Case
3. Homoclinic and Heteroclinic Motions
3.1. Examples and Definitions
3.2. Orbits Homoclinic to Hyperbolic Fixed Points of Ordinary Differential Equations
3.3. Orbits Heteroclinic to Hyperbolic Fixed Points of Ordinary Differential Equations
3.4. Orbits Homoclinic to Periodic Orbits and Invariant Tori
4. Global Perturbation Methods for Detecting Chaotic Dynamics
4.1. The Three Basic Systems and Their Geometrical Structure
4.2. Examples
4.3. Final Remarks
References.