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On thermodynamics of rational maps on the Riemann sphere

Published online by Cambridge University Press:  03 May 2007

TIEN-CUONG DINH
Affiliation:
Analyse Complexe, Plateau 7D, Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013 Paris, France (e-mail: dinh@math.jussieu.fr)
VIÊT-ANH NGUYÊN
Affiliation:
Max-Planck Institut für Mathématik, Vivatsgasse 7, 53111 Bonn, Germany (e-mail: vietanh@mpim-bonn.mpg.de)
NESSIM SIBONY
Affiliation:
Départment de Mathématiques, Bâtiment 425, UMR 8628, Université Paris-Sud, 91405 Orsay, France (e-mail: nessim.sibony@math.u-psud.fr)

Abstract

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.

Type
Research Article
Copyright
2007 Cambridge University Press

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