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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: http://dx.doi.org/10.1090/memo/0844
MathSciNet review: 2184276
MSC: Primary 37J40; Secondary 70H09

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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