Geometry of hyperbolic Julia-Lavaurs setsReport as inadecuate




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1 Department of Mathematics and Statistics Texas Tech 2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

Abstract : Let J σ be the Julia-Lavaurs set of a hyperbolic Lavaurs map gσ be its Hausdorff dimension. We show that the upper ball-box counting dimension and the Hausdorff dimension of Jσ are equal, that the hσ-dimensional Hausdorff measure of J σ vanishes and that the hσ-dimensional packing measure of Jσ is positive and finite. If gσ is derived from the parabolic quadratic polynomial fz = z2 + Image, then the Hausdorff dimension hσ 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.





Author: Mariusz Urbanski - Michel Zinsmeister -

Source: https://hal.archives-ouvertes.fr/



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