Dynamics Reported: Dynamics Reported. New Series, cartea 1

en Limba Engleză Paperback – 28 sep 2011

Dynamics Reported is a series of books dedicated to the exposition of the mathematics of dynamcial systems. Its aim is to make the recent research accessible to advanced students and younger researchers. The series is also a medium for mathematicians to use to keep up-to-date with the work being done in neighboring fields. The style is best described as expository, but complete. Thus, there is an emphasis on examples and explanations, but also theorems normally occur with their proofs. The focus is on the analytic approach to dynamical systems, emphasizing the origins of the subject in the theory of differential equations. Dynamics Reported provides an excellent foundation for seminars on dynamical systems.

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Specificații

ISBN-13: 9783642647581
ISBN-10: 3642647588
Pagini: 264
Ilustrații: IX, 250 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.41 kg
Ediția:Softcover reprint of the original 1st ed. 1992
Editura: Springer
Colecția Dynamics Reported. New Series
Seria Dynamics Reported. New Series

Locul publicării:Berlin, Heidelberg, Germany

Cuprins

Bifurcational Aspects of Parametric Resonance.- 1. Setting of the Problem.- 2. A Normal Form Theory.- 3. Computation of a Third-Order Normal Form.- 4. The Planar Hamilton Form.- 5. Dynamical Conclusions.- A Survey of Normalization Techniques Applied to Perturbed Keplerian Systems.- 1. Introduction.- 2. Perturbed Keplerian Systems.- 3. Normal Form: Theory.- 4. Normal Form: Practice.- 5. Reduction to One Degree of Freedom.- 6. Analysis of Normalized Hamiltonian.- 7. Appendix 1.- 8. Appendix 2.- References.- On Littlewood’s Counterexample of Unbounded Motions in Superquadratic Potentials.- 1. Introduction.- 2. Results.- 3. Proof of the Theorem.- References.- Center Manifold Theory in Infinite Dimensions.- 1. Introduction.- 2. General Theory.- 3. Spectral Theory.- 4. Examples.- 5. Application to Hydrodynamic Stability Problems.- References.- Oscillations in Singularly Perturbed Delay Equations.- 1. Difference Equations.- 2. Singular Perturbations of Difference Equations with Continuous Argument: Simplest Properties.- 3. Continuous Dependence on a Paramete.- 4. Impact of Singular Perturbations: Examples.- 5. Attractors of Interval Maps and Asymptotic Behavior of Solutions.- 6. Existence of Periodic Solutions.- 7. Concluding Remarks and Open Questions.- References.- Topological Approach to Differential Inclusions on Closed Subsets of ?n.- 1. Multivalued Mappings.- 2. Topological Degree of Admissible Mappings in ?n.- 3. Aronszajn’s Result.- 4. Selectionable and ?-Selectionable Multivalued Maps.- 5. Differential Inclusions in ?n.- 6. Periodic Solutions of Differential Inclusions in ?n.- 7. Sets with Property p.- 8. Contingent Cone Valued Maps.- 9. Differential Inclusions on Sets with Property p.- 10. Proof of Lemma (7.3).- References.

Textul de pe ultima copertă

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.