Hausdorff dimension of quadratic rational Julia sets

Authors
Zhou, Jia Liao, Liang Wen
Citation
Zhou, Jia et Liao, Liang Wen, Hausdorff dimension of quadratic rational Julia sets, Acta mathematica Sinica. English series (Print) , 30(2), 2014, pp. 331-342
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
30
Issue
2
Year of publication
2014
Pages
331 - 342
Database
ACNP
SICI code
Abstract
Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two.