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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.

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Ergodicity of conformal measures for unimodal polynomials
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by Eduardo A. Prado
Conform. Geom. Dyn. 2 (1998), 29-44
Published electronically: March 25, 1998


Let $f$ be a polynomial and $\mu$ a conformal measure for $f$, i.e., a Borel probability measure $\mu$ with Jacobian equal to $|Df(z)|^{\delta }$. We show that if $f$ is a real unimodal polynomial (a polynomial with just one critical point), then $\mu$ is ergodic. We also show that $\mu$ is ergodic if $f$ is a complex unimodal polynomial with one parabolic periodic point or a quadratic polynomial in the $\mathcal {SL}$ class with a priori bounds (as defined in Lyubich (1997)).
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Bibliographic Information
  • Eduardo A. Prado
  • Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 CEP 05315-970, São Paulo, Brazil
  • Email:
  • Received by editor(s): September 1, 1997
  • Received by editor(s) in revised form: December 15, 1997
  • Published electronically: March 25, 1998
  • Additional Notes: Supported in part by CNPq-Brazil and S.U.N.Y. at Stony Brook
  • © Copyright 1998 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 2 (1998), 29-44
  • MSC (1991): Primary 58F03, 58F23
  • DOI:
  • MathSciNet review: 1613051