Abstract

Let J σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map g σ be its Hausdorff dimension. We show that the upper ball-(box) counting dimension and the Hausdorff dimension of J σ are equal, that the h σ-dimensional Hausdorff measure of J σ vanishes and that the h σ-dimensional packing measure of J σ is positive and finite. If g σ is derived from the parabolic quadratic polynomial f( z) = z 2 + 1 4 , then the Hausdorff dimension h σ is a real-analytic function of σ. As our tool we study analytic dependence of the Perron-Frobenius operator on the symbolic space with infinite alphabet.

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