The Henon-Heiles system defined on Lie-algebraically deformed Galilei space-time

In this article we provide the Henon-Heiles system defined on Lie-algebraically deformed nonrelativistic space-time with the commutator of two spatial directions proportional to time. Particularly, we demonstrate that in such a model the total energy is not conserved and for this reason the role of...

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Bibliographic Details
Published in:arXiv.org 2017-02
Main Author: Daszkiewicz, Marcin
Format: Article
Language:English
Subjects:
Commutators
Deformation
Energy value
Parameters
Spacetime
Online Access:Get full text
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Summary:In this article we provide the Henon-Heiles system defined on Lie-algebraically deformed nonrelativistic space-time with the commutator of two spatial directions proportional to time. Particularly, we demonstrate that in such a model the total energy is not conserved and for this reason the role of control parameter is taken by the initial energy value \(E_{0,{\rm tot}} = E_{{\rm tot}}(t=0)\). Besides, we show that in contrast with the commutative case, for chosen values of deformation parameter \(\kappa\), there appears chaos in the system for initial total energies \(E_{0,{\rm tot}}\) below the threshold \(E_{0,{\rm th}} = 1/6\).
ISSN:2331-8422
DOI:10.48550/arxiv.1702.08702