  In this paper we implement scale anisotropic transformations in the
space-time in classical mechanics. The resulting system is consistent with the
dispersion relation of gravity at a Lifshitz point recently considered in
arXiv:0901.3775. Also, we show that our model is a generalization of the
conformal mechanics of Alfaro, Fubini and Furlan. For arbitrary $z$ we
construct the dynamical symmetries that correspond to the Schroedinger algebra.
Furthermore, we obtain the Boltzman distribution for a gas of free particles
compatible with anisotropic scaling transformations and compare our result with
the corresponding thermodynamics of the recent anisotropic black branes
proposed in arXiv:0907.4755.
