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Títol: A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model.
Autor: Delshams Valdés, Amadeu Veure Producció científica UPC; Llave Canosa, Rafael de la Veure Producció científica UPC; Martínez-Seara Alonso, M. Teresa Veure Producció científica UPC
Data: 2003
Tipus de document: Article
Resum: We introduce a geometric mechanism for di?usion in a priori unstable nearly integrable dynamical systems. It is based on the observation that resonances, besides destroying the primary KAM tori, create secondary tori and tori of lower dimension. We argue that these objects created by resonances can be incorporated in transition chains taking the place of the destroyed primary KAM tori. We establish rigorously the existence of this mechanism in a simple model that has been studied before. The main technique is to develop a toolkit to study, in a unified way, tori of different topologies and their invariant manifolds, their intersections as well as shadowing properties of these bi-asymptotic orbits. This toolkit is based on extending and unifying standard techniques. A new tool used here is the scattering map of normally hyperbolic invariant manifolds. The model considered is a one-parameter family, which for " = 0 is an integrable system. We give a small number of explicit conditions the jet of order 3 of the family that, if verified imply diffusion. The conditions are just that some explicitely constructed functionals do not vanish identically or have non-degenerate critical points, etc. An attractive feature of the mechanism is that the transition chains are shorter in the places where the heuristic intuition and numerical experimentation suggests that the diffusion is strongest.
URI: http://hdl.handle.net/2117/872
Apareix a les col·leccions:EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions. Articles de revista
Departaments de Matemàtica Aplicada. Articles de revista
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