Elements of Non-Linear Hamiltonian Dynamics

16th Brazilian Colloquium on Orbital Dynamics

De Carvalho, R. Egydio^1

Universidade Estadual Paulista-UNESP, 13506-900 Rio-Claro, SP, Brazil^1

关键词: Hamiltonian dynamics;    Hamiltonian systems;    Isochronous resonances;    meandering tori;    Non-linear dynamics;    Robust tori;    shearless curves;    Transport barrier;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/465/1/012016/pdf
DOI  :  10.1088/1742-6596/465/1/012016

来源: IOP

【 摘 要 】

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.