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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.


Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current
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by Yûsuke Okuyama
Conform. Geom. Dyn. 18 (2014), 217-228
Published electronically: November 12, 2014


We establish an approximation of the activity current $T_c$ in the parameter space of a holomorphic family $f$ of rational functions having a marked critical point $c$ by parameters for which $c$ is periodic under $f$, i.e., is a superattracting periodic point. This partly generalizes a Dujardin–Favre theorem for rational functions having preperiodic points, and refines a Bassanelli–Berteloot theorem on a similar approximation of the bifurcation current $T_f$ of the holomorphic family $f$. The proof is based on a dynamical counterpart of this approximation.
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Bibliographic Information
  • Yûsuke Okuyama
  • Affiliation: Division of Mathematics, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585 Japan
  • Email:
  • Received by editor(s): February 24, 2014
  • Received by editor(s) in revised form: July 11, 2014, and August 12, 2014
  • Published electronically: November 12, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 18 (2014), 217-228
  • MSC (2010): Primary 37F45
  • DOI:
  • MathSciNet review: 3276585