Elements of Non-Linear Hamiltonian Dynamics
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Undergraduate course
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Iop Publishing Ltd
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Abstract
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.
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Keywords
isochronous resonances, robust torus, meandering tori, shearless curves
Language
English
Citation
Xvi Brazilian Colloquium On Orbital Dynamics. Bristol: Iop Publishing Ltd, v. 465, 6 p., 2013.
