On Thermodynamics of Rational Maps on the Riemann sphere

Nessim Sibony; Tien-Cuong Dinh; Viet-Anh Nguyen

arxiv: math/0603507 · v1 · submitted 2006-03-21 · 🧮 math.DS · math.CV

On Thermodynamics of Rational Maps on the Riemann sphere

Tien-Cuong Dinh , Viet-Anh Nguyen , Nessim Sibony This is my paper

classification 🧮 math.DS math.CV

keywords rationalriemannsphereassociatedcentralconvergenceentropyestablish

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We show that there is a spectral gap for the transfer operator associated to a rational map f on the Riemann sphere. Using this and the method of pertubed operators we establish the (Local) Central Limit Theorem for the measure of maximal entropy of f, with an estimate on the speed of convergence.

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On Thermodynamics of Rational Maps on the Riemann sphere

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