Dynamics Reported: Expositions in Dynamical Systems: 2 - Brossura

Brossura

ISBN 10: 3642647553 ISBN 13: 9783642647550

Casa editrice: Springer, 2011

Riassunto

This book contains four contributions in the field of dynamical systems. The topics treated are also related to functional analysis, probabability theory, Hamiltonian systems, and classical mechanics. All the authors give a careful and readable presentation of recent research results, which are of interest to mathematicians and physicists alike. The book is written for graduate students and researchers in mathematics and physics and it is also suitable as a text for graduate level seminars in dynamical systems.

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Contenuti

Transversal Homoclinic Orbits near Elliptic Fixed Points of Area-preserving Diffeomorphisms of the Plane.- 1. Introduction.- 2. Elements of the Theory of Minimal States.- 3. A Priori Lipschitz Estimates for Minimal Orbits.- 4. First Perturbation: Isolation and Hyperbolicity of Minimal Periodic Orbits.- 5. Second Perturbation: Nondegeneracy of Homoclinic Orbits.- 6. Application to Mather Sets.- 7. Special Classes of Diffeomorphisms.- References.- Asymptotic Periodicity of Markov and Related Operators.- 1. Basic Notions and Results.- 2. The Reduction Procedure.- 3. Asymptotic Periodicity of Constrictive Marcov Operators.- 4. Weakly Almost Periodic Operators.- 5. Asymptotic Periodicity of Power Bounded Operators.- 6. Asymptotic Periodicity of Operators on Signed Measures.- References.- A Nekhoroshev-Like Theory of Classical Particle Channeling in Perfect Crystals.- I. Introduction.- 2. Background and Outline of Main Results.- 2.1 Sketch of the Development of Nekhoroshev Theory.- 2.2 Brief Description of the Physics of Particle Channeling in Crystals..- 2.3 Outline of Main Results.- 3. Formulation of the Channeling Problem.- 3.1 The Perfect Crystal Model.- 3.2 The Channeling Criterion.- 3.3 Transformation to Nearly Integrable Form.- 4. Construction of the Normal Forms.- 4.1 Description of Methods.- 4.2 Notation.- 4.3 Near Identity Canonical Transformations via the Lie Method.- 4.4 Statement of the Analytic Lemma.- 4.5 The Iterative Lemma.- 4.6 Technical Estimates.- 4.7 Proof of the Analytic Lemma.- 5. The Generalized Continuum Models.- 5.1 Resonant Zones and Resonant Blocks.- 5.2 Geometric Considerations.- 5.3 The Spatial Continuum Model.- 5.4 Channeling.- 6. Concluding Remarks.- References.- The Adiabatic Invariant in Classical Mechanics.- I The Classical Adiabatic Invariant Theory.- 1. Introduction.- 2. Action-Angle Variables.- 3. Perturbation Theory.- 4. The Adiabatic Invariant.- 5. Explicit Approach to Action-Angle Variables.- 6. Extension of Perturbation Theory to the Case of Unbounded Period.- II Transition Through a Critical Curce.- 1. Introduction.- 2. Neighborhood of an Homoclinic Orbit.- 3. The Autonomous Problem Close to the Equilibrium.- 4. The Autonomous Problem Close to the Homoclinic Orbit.- 5. Traverse from Apex to Apex.- 6. Probability of Capture.- 7. Time of Transit.- 8. Change in the Invariant.- III The Paradigms.- 1. Introduction.- 2. The Pendulum.- 3. The Second Fundamental Model.- 4. The Colombo’s Top.- 5. Dissipative Forces.- IV Applications.- 1. Introduction.- 2. Passage Through Resonance of a Forced Anharmonic Oscillator.- 3. Particle Motion in a Slowly Modulated Wave.- 4. The Magnetic Bottle.- 5. Orbit-Orbit Resonances in the Solar System.- 6. Spin-Orbit Resonance in the Solar System.- Appendix 1: Variational Equations.- Appendix 2: Fixing the Unstable Equilibrium and the Time Scale..- Appendix 3: Mean Value of Ri(?i, Ji, ?) 1?i?2.- Appendix 4: Mean Value of R3 (?3, J3, ?).- Appendix 5: Estimation of the Trajectory Close to the Equilibrium..- Appendix 6: Computation of the True Time of Transit.- Appendix 7: The Diffusion Parameter in Non-Symmetric Cases.- Appendix 8: Remarks on the Paper “On the Generalization of a Theorem of A. Liapounoff”, by J. Moser (Comm. P. Appl. Math. 9, 257-271, 1958).- References.- List of Contributors.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3642647553
• ISBN 13: 9783642647550
• Rilegatura: Copertina flessibile
• Numero di pagine: 252
• Contatto del produttore: non disponibile
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