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

## TL;DR

This paper explores the Henon-Heiles system on a Lie-algebraically deformed Galilei space-time, revealing non-conservation of energy and the emergence of chaos at certain energy thresholds due to space-time deformation.

## Contribution

It introduces a novel formulation of the Henon-Heiles system on a deformed nonrelativistic space-time and analyzes how deformation affects energy conservation and chaotic behavior.

## Key findings

- Energy is not conserved in the deformed system.
- Chaos appears below a specific energy threshold due to deformation.
- Deformation parameter influences the onset of chaos.

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