Large deviations and a fluctuation symmetry for chaotic homeomorphisms

We consider expansive homeomorphisms with the specification property. We give a new simple proof of a large deviation principle for Gibbs measures corresponding to. a regular potential and we establish a general symmetry of the rate function for the large deviations of the antisymmetric part, under time-reversal, of the potential. This generalizes the Gallavotti-Cohen fluctuation theorem to a larger class of chaotic systems.