## Ergodicity of conformal measures for unimodal polynomials

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- by Eduardo A. Prado
- Conform. Geom. Dyn.
**2**(1998), 29-44 - DOI: https://doi.org/10.1090/S1088-4173-98-00019-8
- Published electronically: March 25, 1998
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## 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

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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: prado@ime.usp.br
- 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: https://doi.org/10.1090/S1088-4173-98-00019-8
- MathSciNet review: 1613051