Resumen de The rényi entropy function and the large deviation of short return times

Nicolai Haydn, S. Vaienti

• We consider the Rényi entropy function for weakly psi-mixing systems. The first main result of the paper establishes existence and regularity properties. The second main result is obtaining the decay rate for the large deviation of the return time to cylinder sets; we show that it is exponential with a rate given by the Rényi entropy function. Finally, we also obtain bounds for the free energy.