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A geometric mechanism of diffusion: rigorous verification in a priori unstable Hamiltonian systems
Delshams Valdés, Amadeu; Huguet Casades, Gemma
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística
Hamiltonian systems
Sistemes dinàmics diferenciables
Equacions diferencials
Hamilton, Sistemes de
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