Geometry of hyperbolic Julia-Lavaurs sets
type: Item
instance of: scholarly article
title: Geometry of hyperbolic Julia-Lavaurs sets
zbMATH Open document ID: 1005.37020
DOI: 10.1016/S0019-3577(01)80032-X
author: Michel Zinsmeister
author: Mariusz Urbański
published in: Indagationes Mathematicae. New Series
publication date: 2002-06-23T00:00:00Z
review text: This paper deals with the properties of the Lavaurs map. Indeed let \(J_\sigma\) be the Julia-Lavaurs set of a hyperbolic map \(g_\sigma\) and let \(h_\sigma\) be its Hausdorff dimension. The authors show that the upper ball-(box) counting dimension and the Hausdorff dimension of \(J_\sigma\) are equal. Moreover, they show, if \(g_\sigma\) is derived from the parabolic quadratic polynomial \(f(z)= z^2+ \frac 14\), then the Hausdorff dimension \(h_\sigma\) is a real-analytic function of \(\sigma\). To this end, the authors study analytic dependence of the Perron-Frobenius operator on the symbolic space with infinite alphabet.
Mathematics Subject Classification ID: 37F35
Mathematics Subject Classification ID: 37F50
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 1758191
zbMATH Keywords: Lavaurs map
zbMATH Keywords: Julia-Lavaurs set
zbMATH Keywords: hyperbolic map
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: upper ball-(box) counting dimension
zbMATH Keywords: Perron-Frobenius operator
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
Wikidata QID: Q121087571
cites work: Lectures on hyperbolic geometry
cites work: Q4328166
cites work: Q3345037
cites work: Q3688631
cites work: Implosion parabolique et dimension de Hausdorff
cites work: Perturbation theory for linear operators.
cites work: Dimensions and Measures in Infinite Iterated Function Systems
cites work: Conformal iterated function systems with applications to the geometry of continued fractions
cites work: Q4000499
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description: scientific article; zbMATH DE number 1758191