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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.

Copyright 2003 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 09 (2003), pp. 125-134
• Publisher Identifier: S 1079-6762(03)00121-5
• 2000 Mathematics Subject Classification. Primary 37J40; Secondary 70H08, 37D10, 70K70
• Key words and phrases. Nearly integrable Hamiltonian systems, normal forms, slow variables, normally hyperbolic invariant manifolds, KAM theory, Arnold diffusion
• Received by editors March 9, 2003
• Received by editors in revised form September 19, 2003
• Posted on December 4, 2003
• Communicated by Svetlana Katok
• Comments (When Available)

Amadeu Delshams

Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

E-mail address: Amadeu.Delshams@upc.es

Rafael de la Llave

Department of Mathematics, University of Texas, Austin, TX 78712-1802

E-mail address: llave@math.utexas.edu

Tere M. Seara

Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

E-mail address: tere.m-seara@upc.es