The generalized thermodynamics formalism applied to hyperbolic and nonhyperbolic models

In this paper, scaling properties of hyperbolic and nonhyperbolic model systems are discussed by using the generalized thermodynamic formalism. The central quantity for the investigation is the generalized entropy function. With the help of this approach, insight into the possible occurrence of phase trnasitions in the various entropy-like scaling functions can be gained. It is shown how this effect is determined by the existence of a critical line in the surface described by the generalized entropy function