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TitleDynamics Reported [electronic resource] : Expositions in Dynamical Systems / edited by Christopher K. R. T. Jones, Urs Kirchgraber, Hans-Otto Walther
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1996
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Descript IX, 287 p. online resource


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 with Weakly Expanding Center Manifolds" and "Homoclinic Orbits in a Four-Dimensional Model of a Perturbed NLS Equation: A Geometric Singular Perturbation Study". All the authors give a careful and readable presentation of recent research results, addressed not only to specialists but also to a broader range of readers including graduate students


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 qโ{130}ฌ -- 6. Numerical Study of Orbits Homoclinic to qโ{130}ฌ -- 7. The Dynamical Consequences of Orbits Homoclinic to qโ{130}ฌ: The Existence and Nature of Chaos -- 8. Conclusion -- References

Mathematics Mathematical analysis Analysis (Mathematics) Manifolds (Mathematics) Complex manifolds Physics Mathematics Analysis Manifolds and Cell Complexes (incl. Diff.Topology) Theoretical Mathematical and Computational Physics


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