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On Iterated Function Systems with place-dependent probabilities

Author: Balázs Bárány
Journal: Proc. Amer. Math. Soc. 143 (2015), 419-432
MSC (2010): Primary 60G30; Secondary 28A80
Published electronically: August 22, 2014
MathSciNet review: 3272766
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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.

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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

Keywords: Iterated function systems, place-dependent probabilities, Hausdorff dimension, absolute continuity
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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