Geometry of hyperbolic Julia-Lavaurs sets
Urbanski, Mariusz ; Zinsmeister, Michel
HAL, hal-00079633 / Harvested from HAL
Text on HAL
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 f(z) = 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.
Publié le : 2001-07-05
Classification:  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 
@article{hal-00079633,
     author = {Urbanski, Mariusz and Zinsmeister, Michel},
     title = {Geometry of hyperbolic Julia-Lavaurs sets},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00079633}
}

Urbanski, Mariusz; Zinsmeister, Michel. Geometry of hyperbolic Julia-Lavaurs sets. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00079633/