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In this article we provide the Henon-Heiles system defined onLie-algebraically deformed nonrelativistic space-time with the commutator oftwo spatial directions proportional to time. Particularly, we demonstrate thatin such a model the total energy is not conserved and for this reason the roleof 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 commutativecase, for chosen values of deformation parameter $\kappa$, there appears chaosin the system for initial total energies $E_{0,{\rm tot}}$ below the threshold$E_{0,{\rm th}} = 1/6$.

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