Elements of Non-Linear Hamiltonian Dynamics

• Autor(a) principal: Egydio de Carvalho, R.
• Data de Publicação: 2013
• Outros Autores: IOP
• Tipo de documento: Artigo de conferência
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1088/1742-6596/465/1/012016; http://hdl.handle.net/11449/111529
• topic: isochronous resonances; robust torus; meandering tori; shearless curves

In this paper we present a set of generic results on Hamiltonian non-linear dynamics. We show the necessary conditions for a Hamiltonian system to present a non-twist scenario and from that we introduce the isochronous resonances. The generality of these resonances is shown from the Hamiltonian given by the Birkhof-Gustavson normal form, which can be considered a toy model, and from an optic system governed by the non-linear map of the annular billiard. We also define a special kind of transport barrier called robust torus. The meanders and shearless curves are also presented and we show the most robust shearless barrier associated with the rotation numbers.