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A geometric mechanism of diffusion: rigorous verification in a priori unstable Hamiltonian systems

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10.1016/j.jde.2010.12.023
 
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Delshams Valdés, AmadeuMés informacióMés informacióMés informació
Huguet Casades, GemmaMés informacióMés informacióMés informació
Document typeArticle
Defense date2011-03-01
Rights accessRestricted access - publisher's policy
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
In this paper we consider a representative a priori unstable Hamiltonian system with 2 + 1/2 degrees of freedom and we apply the geometric mechanism for diffusion introduced in [A. Delshams, R. de la Llave, T.M. Seara, A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model, Mem. Amer. Math. Soc. 179 (844) (2006), viii + 141 pp.], and generalized in [A. Delshams, G. Huguet, Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems, Nonlinearity 22 (8) (2009) 1997– 2077]. We provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform the straightforward computations along the proof and present the geometric mechanism of diffusion in an easily understandable way. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.
CitationDelshams, A.; Huguet, G. A geometric mechanism of diffusion: rigorous verification in a priori unstable Hamiltonian systems. "Journal of differential equations", 01 Març 2011, vol. 250, núm. 5, p. 2601-2623. 
URIhttp://hdl.handle.net/2117/11567
DOI10.1016/j.jde.2010.12.023
ISSN0022-0396
Publisher versionhttp://linkinghub.elsevier.com/retrieve/pii/S0022039610004730
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  • EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions - Articles de revista [416]
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