论文信息 - On the transfer operator for rational functions on the Riemann sphere

On the transfer operator for rational functions on the Riemann sphere

Let T be a rational function of degree 2 on the Riemann sphere. Denote L the transfer operator of a HH older-continuous function on its Julia set J = J(T) satisfying P(T;) > sup z2J (z). We study the behavior of fL n : n 1g for HH older-continuous functions and show that the sequence is (uniformly) norm-bounded in the space of HH older-continuous functions for suuciently small exponent. As a consequence we obtain that the density of the equilibrium measure for with respect to the exppP(T;) ? ]-conformal measure is HH older-continuous. We also prove that the rate of convergence of L n to this density in sup-norm is O ? exp(? p n). >From this we deduce the central limit theorem for .

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