On Iterated Function Systems with place-dependent probabilities
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- by Balázs Bárány
- Proc. Amer. Math. Soc. 143 (2015), 419-432
- DOI: https://doi.org/10.1090/S0002-9939-2014-12193-9
- Published electronically: August 22, 2014
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Corrigendum: Proc. Amer. Math. Soc. 150 (2022), 5483-5483.
Abstract:
In this paper we study a family of invariant measures of parameterized iterated function systems where the corresponding probabilities are place-dependent. We prove that the Hausdorff dimension of the measure is equal to entropy/Lyapunov exponent whenever it is less than $1$ and the measure is absolute continuous w.r.t. the Lebesgue measure if entropy/Lyapunov exponent is greater than $1$ for Lebesgue almost every parameters.References
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Bibliographic Information
- Balázs Bárány
- Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Sńiadeckich 8, P. O. Box 21, 00-956 Warszawa, Poland
- Address at time of publication: Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
- MR Author ID: 890989
- Email: balubsheep@gmail.com
- Received by editor(s): October 16, 2012
- Received by editor(s) in revised form: March 1, 2013
- Published electronically: August 22, 2014
- Communicated by: Nimish Shah
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 419-432
- MSC (2010): Primary 60G30; Secondary 28A80
- DOI: https://doi.org/10.1090/S0002-9939-2014-12193-9
- MathSciNet review: 3272766