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A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results

Author(s): Amadeu Delshams; Rafael de la Llave; Tere M. Seara
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 125-134.
MSC (2000): Primary 37J40; Secondary 70H08, 37D10, 70K70
Posted: December 4, 2003
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Abstract: We present a geometric mechanism for diffusion in Hamiltonian systems. We also present tools that allow us to verify it in a concrete model. In particular, we verify it in a system which presents the large gap problem.

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Additional Information:

Amadeu Delshams
Affiliation: Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
Email: Amadeu.Delshams@upc.es

Rafael de la Llave
Affiliation: Department of Mathematics, University of Texas, Austin, TX 78712-1802
Email: llave@math.utexas.edu

Tere M. Seara
Affiliation: Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
Email: tere.m-seara@upc.es

DOI: 10.1090/S1079-6762-03-00121-5
PII: S 1079-6762(03)00121-5
Keywords: Nearly integrable Hamiltonian systems, normal forms, slow variables, normally hyperbolic invariant manifolds, KAM theory, Arnold diffusion
Received by editor(s): March 9, 2003
Received by editor(s) in revised form: September 19, 2003
Posted: December 4, 2003
Communicated by: Svetlana Katok
Copyright of article: Copyright 2003, American Mathematical Society

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