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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase
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by Mariusz Urbanski and Michel Zinsmeister
Conform. Geom. Dyn. 5 (2001), 140-152
Published electronically: October 18, 2001


Let $f_{0}(z)=z^{2}+1/4$ and ${\mathcal E}_{0}$ the set of phases $\overline {\sigma }$ such that the critical point $0$ escapes in one step by the Lavaurs map $g_{\sigma }$; it is a topological strip in the cylinder of phases whose boundary consists of two Jordan curves symmetric wrt $\mathbb R/ \mathbb Z$. We prove that if $\overline {\sigma }_{n}\in {\mathcal E}_{0}$ converges to $\overline {\sigma }\in \partial {\mathcal E}_{0}$ in such a way that $g_{\sigma _{n}}(0)$ converges to $g_{\sigma }(0)$ along an external ray, then the Hausdorff dimension of the Julia-Lavaurs set $J(f_{0}, g_{\sigma _{n}})$ converges to the Hausdorff dimension of $J(f_{0},g_{\sigma })$.
    uz0 Adrien Douady: Does a Julia set depend continuously on the polynomial? Proceedings of Symposia in Applied Mathematics 49 (1994), 91–135. uz1 Pierre Lavaurs: Systèmes dynamiques holomorphes: explosion de points périodiques paraboliques. These, Université Paris-Sud, 1989. uz5 Mariusz Urbanski and Michel Zinsmeister: Geometry of hyperbolic Julia-Lavaurs sets, Preprint 2000, to appear Indagationes Math.
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Bibliographic Information
  • Mariusz Urbanski
  • Affiliation: Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, Texas 76203-1430
  • Email:
  • Michel Zinsmeister
  • Affiliation: Mathématiques, Université d’Orleans, BP 6759 45067 Orléans Cedex, France
  • Email:
  • Received by editor(s): September 18, 2000
  • Received by editor(s) in revised form: June 28, 2001
  • Published electronically: October 18, 2001
  • Additional Notes: The research of the first author was partially supported by the NSF Grant DMS 9801583. He wishes to thank the University of Orleans and IHES, where a part of the research was done, for warm hospitality and excellent working conditions
  • © Copyright 2001 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 5 (2001), 140-152
  • MSC (2000): Primary 37F45; Secondary 37F35, 37F15
  • DOI:
  • MathSciNet review: 1872160