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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.


Real entropy rigidity under quasi-conformal deformations
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by Khashayar Filom
Conform. Geom. Dyn. 25 (2021), 1-33
Published electronically: March 9, 2021


We set up a real entropy function $h_\Bbb {R}$ on the space $\mathcal {M}’_d$ of Möbius conjugacy classes of real rational maps of degree $d$ by assigning to each class the real entropy of a representative $f\in \Bbb {R}(z)$; namely, the topological entropy of its restriction $f\restriction _{\hat {\Bbb {R}}}$ to the real circle. We prove a rigidity result stating that $h_\Bbb {R}$ is locally constant on the subspace determined by real maps quasi-conformally conjugate to $f$. As examples of this result, we analyze real analytic stable families of hyperbolic and flexible Lattès maps with real coefficients along with numerous families of degree $d$ real maps of real entropy $\log (d)$. The latter discussion moreover entails a complete classification of maps of maximal real entropy.
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Bibliographic Information
  • Khashayar Filom
  • Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109
  • MR Author ID: 1190306
  • Email:
  • Received by editor(s): May 4, 2019
  • Received by editor(s) in revised form: December 1, 2020
  • Published electronically: March 9, 2021
  • © Copyright 2021 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 25 (2021), 1-33
  • MSC (2020): Primary 37B40, 37E10, 37F31; Secondary 37F10, 37P45
  • DOI:
  • MathSciNet review: 4294970