On thermodynamics of rational maps on the Riemann sphere

• Autores: Tien-Cuong Dinh, Viêt-Anh Nguyên, Nessim Sibony
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 4, 2007, págs. 1095-1109
• Idioma: inglés
• DOI: 10.1017/s0143385706001003
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• Resumen

  • 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.