The Henon-Heiles system defined on Lie-algebraically deformed Galilei spacetime. (English) Zbl 1372.37107
Summary: In this paper, we provide the Henon-Heiles system defined on Lie-algebraically deformed non-relativistic spacetime 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 \(E_{0,\mathrm{th}}=1/6\).
MSC:
| 37J15 | Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010) |
| 70G65 | Symmetries, Lie group and Lie algebra methods for problems in mechanics |
| 83C65 | Methods of noncommutative geometry in general relativity |
| 70H05 | Hamilton’s equations |
| 16T05 | Hopf algebras and their applications |
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