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arXiv · 1702.08702

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

Marcin Daszkiewicz
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Abstract

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 $κ$, there appears chaos in the system for initial total energies $E_{0,{\rm tot}}$ below the threshold $E_{0,{\rm th}} = 1/6$.

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Marcin Daszkiewicz. 2017-02-28. The Henon-Heiles system defined on Lie-algebraically deformed Galilei space-time. https://doi.org/10.1142/s0217732317500754

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