Resumen de On thermodynamics of rational maps on the Riemann sphere

Tien-Cuong Dinh, Viêt-Anh Nguyên, Nessim Sibony

• We show that there is a spectral gap for the transfer operator associated with a rational map $f$ on the Riemann sphere. Using this and the method of perturbed operators, we establish the (local) central limit theorem for the measure of maximal entropy of $f$, with an estimate on the speed of convergence.