Arnold diffusion for a complete family of perturbations with two independent harmonics

Delshams Valdés, Amadeu; Gonçalves Schaefer, Rodrigo

doi:10.3934/dcds.2018261

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Delshams Valdés, Amadeu

Gonçalves Schaefer, Rodrigo

Document typeArticle

Defense date2018-12-01

PublisherAmerican Institute of Mathematical Sciences

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

We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several scattering maps. A complete description of the different kinds of scattering maps taking place as well as the existence of piecewise smooth global scattering maps is also provided

CitationDelshams, A., Gonçalves, R. Arnold diffusion for a complete family of perturbations with two independent harmonics. "Discrete and continuous dynamical systems. Series A", 1 Desembre 2018, vol. 38, núm. 12, p. 6047-6072.

URIhttp://hdl.handle.net/2117/126910

DOI10.3934/dcds.2018261

ISSN1078-0947

Publisher versionhttp://aimsciences.org//article/doi/10.3934/dcds.2018261

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