Conformal anisotropic mechanics and the Horava dispersion relation

In this paper we implement scale anisotropic transformations between space and time in classical mechanics. The resulting system is consistent with the dispersion relation of Horava gravity [P. Horava, Phys. Rev. D 79, 084008 (2009)]. Also, we show that our model is a generalization of the conformal mechanics of Alfaro, Fubini, and Furlan. For an arbitrary dynamical exponent we construct the dynamical symmetries that correspond to the Schroedinger algebra. Furthermore, we obtain the Boltzmann 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 the literature.