Author | Wiggins, Stephen. author |
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Title | Global Bifurcations and Chaos [electronic resource] : Analytical Methods / by Stephen Wiggins |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1042-9 |
Descript | XIV, 495 p. online resource |
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. Poincarรฉ 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