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

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hdl:2117/8414
Document typeResearch report
Defense date2010-07
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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]
URL other repositoryhttp://www.ma1.upc.edu/recerca/preprints/2010/prepr201001delshams.pdf
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