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

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 $E_{0,\mathrm{tot}}=E_{\mathrm{tot}}(t=0)$. 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 $E_{0,\mathrm{tot}}$ below the threshold $E_{0,\mathrm{th}}=1/6$.

Latex source, 18 pages, 8 figures, paper accepted for publication in MPLA. arXiv admin note: substantial text overlap with arXiv:1610.08361

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Cited by in corpus (2)

• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system