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

• Record Nr.: UNINA9910480091103321
• Autore: Delshams Amadeu
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2006
• ISBN: 1-4704-0445-1
• Descrizione fisica: 1 online resource (158 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 844
• Disciplina: 510 s; 515/.39
• Soggetti: Nonholonomic dynamical systems; Mechanics; Differential equations - Qualitative theory; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• 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""