Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Ergodicity of conformal measures for unimodal polynomials


Author: Eduardo A. Prado
Journal: Conform. Geom. Dyn. 2 (1998), 29-44
MSC (1991): Primary 58F03, 58F23
Published electronically: March 25, 1998
MathSciNet review: 1613051
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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)).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (1991): 58F03, 58F23

Retrieve articles in all journals with MSC (1991): 58F03, 58F23


Additional Information

Eduardo A. Prado
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281 CEP 05315-970, São Paulo, Brazil
Email: prado@ime.usp.br

DOI: http://dx.doi.org/10.1090/S1088-4173-98-00019-8
PII: S 1088-4173(98)00019-8
Keywords: Holomorphic dynamics, conformal measures
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
Article copyright: © Copyright 1998 American Mathematical Society