On Thermodynamics of Rational Maps on the Riemann sphere

Details On Thermodynamics of Rational Maps on the Riemann sphere On Thermodynamics of Rational Maps on the Riemann sphere

2006-03-21

arxiv.org/abs/math/0603507v1

Mathematics

Dynamical Systems

17 pages

Scientific paper

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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