Dynamics Reported
Expositions in Dynamical Systems
Springer (Publisher)
Published on 14. December 2011
Book
Paperback/Softback
IX, 289 pages
978-3-642-79933-4 (ISBN)
Description
DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dynam ical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed expo sition of ideas, restriction to typical results - rather than the most general ones - and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents Hyperbolicity and Exponential Dichotomy for Dynamical Systems Neil Fenichel 1. Introduction . . . . . . . . . . . . . . . . . . I 2. The Main Lemma . . . . . . . . . . . . . . . . 2 3. The Linearization Theorem of Hartman and Grobman 5 4. Hyperbolic Invariant Sets: ?-orbits and Stable Manifolds 6 5.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1996
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
IX, 289 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 17 mm
Weight
464 gr
ISBN-13
978-3-642-79933-4 (9783642799334)
DOI
10.1007/978-3-642-79931-0
Schweitzer Classification
Other editions
Additional editions
Dynamics Reported
Expositions in Dynamical Systems
Book
04/1996
Springer
€117.69
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Content
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.