Dynamics Reported: Expositions in Dynamical Systems: Dynamics Reported. New Series, cartea 2
Contribuţii de H.S. Dumas, C. Genecand, J. Henrard, J. Komorniken Limba Engleză Paperback – 16 sep 2011
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Specificații
ISBN-13: 9783642647550
ISBN-10: 3642647553
Pagini: 252
Ilustrații: IX, 235 p.
Dimensiuni: 170 x 242 x 13 mm
Greutate: 0.41 kg
Ediția:Softcover reprint of the original 1st ed. 1993
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Dynamics Reported. New Series
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3642647553
Pagini: 252
Ilustrații: IX, 235 p.
Dimensiuni: 170 x 242 x 13 mm
Greutate: 0.41 kg
Ediția:Softcover reprint of the original 1st ed. 1993
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Dynamics Reported. New Series
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
ResearchCuprins
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.- 3. Formulation of the Channeling Problem.- 4. Construction of the Normal Forms.- 5. The Generalized Continuum Models.- 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.