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A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model
About this Title
Amadeu Delshams, Rafael de la Llave and Tere M. Seara
Publication: Memoirs of the American Mathematical Society
Publication Year:
2006; Volume 179, Number 844
ISBNs: 978-0-8218-3824-2 (print); 978-1-4704-0445-1 (online)
DOI: https://doi.org/10.1090/memo/0844
MathSciNet review: 2184276
MSC: Primary 37J40; Secondary 70H09
Table of Contents
Chapters
- 1. Introduction
- 2. Heuristic discussion of the mechanism
- 3. A simple model
- 4. Statement of rigorous results
- 5. Notation and definitions, resonances
- 6. Geometric features of the unperturbed problem
- 7. Persistence of the normally hyperbolic invariant manifold and its stable and unstable manifolds
- 8. The dynamics in $\tilde {\Lambda }_\epsilon$
- 9. The scattering map
- 10. Existence of transition chains
- 11. Orbits shadowing the transition chains and proof of Theorem 4.1
- 12. Conclusions and remarks
- 13. An example