98-408 N T A Haydn

Statistical properties of equilibrium states for rational maps (43K, LATeX 2e) Jun 1, 98

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Abstract. Equilibrium states of rational maps H\"older continuous potentials that satisfies the `supremum gap' are not $\phi$-mixing, mainly due to the presence of critical points. Here we prove that the normalised return times of arbitrary orders are in the limit Poisson distributed. We also show that the usual generating partition is weakly Bernoulli, from which the Bernoulli-ness then follows by a standard result.

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