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

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hdl:2117/8414

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Delshams Valdés, AmadeuMés informacióMés informacióMés informació
Huguet Casades, GemmaMés informacióMés informacióMés informació
Document typeResearch report
Defense date2010-07
Rights accessOpen Access
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, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. 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.
Is part of[prepr201004DelH]
URIhttp://hdl.handle.net/2117/8414
URL other repositoryhttp://www.ma1.upc.edu/recerca/preprints/2010/prepr201001delshams.pdf
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