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Dynamics Reported Expositions in Dynamical Systems

This book contains four excellent contributions on topics in dynamical systems by authors with an international reputation: "Hyperbolic and Exponential Dichotomy for Dynamical Systems", "Feedback Stabilizability of Time-periodic Parabolic Equations", "Homoclinic Bifurcations...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1996, 1996
Edition:1st ed. 1996
Series:Dynamics Reported. New Series, Expositions in Dynamical Systems
Subjects:
Mathematical Analysis
Analysis
Mathematical Physics
Manifolds And Cell Complexes
Manifolds (mathematics)
Theoretical, Mathematical And Computational Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Hyperbolicity and Exponential Dichotomy for Dynamical Systems
  • 1. Introduction
  • 2. The Main Lemma
  • 3. The Linearization Theorem of Hartman and Grobman
  • 4. Hyperbolic Invariant Sets: e-orbits and Stable Manifolds
  • 5. Structural Stability of Anosov Diffeomorphisms
  • 6. Periodic Points of Anosov Diffeomorphisms
  • 7. Axiom A Diffeomorphisms: Spectral Decomposition
  • 8. The In-Phase Theorem
  • 9. Flows
  • 10. Proof of Lemma 1
  • References
  • Feedback Stabilizability of Time-Periodic ParabolicEquations
  • 0. Introduction
  • I. Linear Periodic Evolution Equations
  • II. Controllability, Observability and Feedback Stabilizability
  • III. Applications to Second Order Time-Periodic Parabolic Initial-Boundary Value Problems
  • References
  • Homoclinic Bifurcations with Weakly Expanding Center
  • 1. Introduction
  • 2. Hypotheses, a Reduction Principle and Basic Existence Theorems
  • 3. Preliminaries
  • 4. Proof of the Main Results in 2
  • 5. Simple Periodic Solutions
  • 6. Bifurcations of Homoclinic Solutions with One-Dimensional Local Center Manifolds
  • 7. Estimates Related to a Nondegenerate Hopf Bifurcation
  • 8. Interaction of Homoclinic Bifurcation and Hopf Bifurcation
  • 9. The Disappearance of Periodic and Aperiodic Solutions when ?2 Passes Through Turning Points
  • References
  • Homoclinic Orbits in a Four Dimensional Model of a Perturbed NLS Equation: A Geometric Singular Perturbation Study
  • 1. Introduction
  • 2. Geometric Structure and Dynamics of the Unperturbed System
  • 3. Geometric Structure and Dynamics of the Perturbed System
  • 4. Fiber Representations of Stable and Unstable Manifolds
  • 5. Orbits Homoclinic to q€
  • 6. Numerical Study of Orbits Homoclinic to q€
  • 7. The Dynamical Consequences of Orbits Homoclinic to q€: The Existence and Nature of Chaos
  • 8. Conclusion.-References

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