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A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara



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Autore: Delshams Amadeu Visualizza persona
Titolo: A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem : heuristics and rigorous verification on a model / / Amadeu Delshams, Rafael de la Llave, Tere M. Seara Visualizza cluster
Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2006
Descrizione fisica: 1 online resource (158 p.)
Disciplina: 510 s
515/.39
Soggetto topico: Nonholonomic dynamical systems
Mechanics
Differential equations - Qualitative theory
Persona (resp. second.): De la LlaveRafael <1957->
SearaTere M. <1961->
Note generali: "January 2006, volume 179, number 844 (third of 5 numbers)."
Nota di bibliografia: Includes bibliographical references (pages 137-141).
Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Heuristic discussion of the mechanism""; ""2.1. Integrable systems, resonances, secondary tori""; ""2.2. Heuristic description of the mechanism""; ""Chapter 3. A simple model""; ""Chapter 4. Statement of rigorous results""; ""Chapter 5. Notation and definitions, resonances""; ""Chapter 6. Geometric features of the unperturbed problem""; ""Chapter 7. Persistence of the normally hyperbolic invariant manifold and its stable and unstable manifolds""; ""7.1. Explicit calculations of the perturbed invariant manifold""
""8.5.2. Preliminary analysis of resonances of order one or two""""8.5.3. Primary and secondary tori near the first and second order resonances""; ""8.5.4. Proof of Theorem 8.30 and Corollary 8.31""; ""8.5.5. Existence of stable and unstable manifolds of periodic orbits""; ""Chapter 9. The scattering map""; ""9.1. Some generalities about the scattering map""; ""9.2. The scattering map in our model: definition and computation""; ""Chapter 10. Existence of transition chains""; ""10.1. Transition chains""; ""10.2. The scattering map and the transversality of heteroclinic intersections""
""10.2.1. The non-resonant region and resonances of order 3 and higher""""10.2.2. Resonances of first order""; ""10.2.3. Resonances of order 2""; ""10.3. Existence of transition chains to objects of different topological types""; ""Chapter 11. Orbits shadowing the transition chains and proof of theorem 4.1""; ""Chapter 12. Conclusions and remarks""; ""12.1. The role of secondary tori and the speed of diffusion""; ""12.2. Comparison with [DLS00]""; ""12.3. Heuristics on the genericity properties of the hypothesis and the phenomena""; ""12.4. The hypothesis of polynomial perturbations""
""12.5. Involving other objects""""12.6. Variational methods""; ""12.7. Diffusion times""; ""Chapter 13. An example""; ""Acknowledgments""; ""Bibliography""
Titolo autorizzato: A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem  Visualizza cluster
ISBN: 1-4704-0445-1
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910788741103321
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Serie: Memoirs of the American Mathematical Society ; ; no. 844.