Hausdorff dimension of the limit set of conformal iterated function systems with overlaps
HTML articles powered by AMS MathViewer
- by Eugen Mihailescu and Mariusz Urbański PDF
- Proc. Amer. Math. Soc. 139 (2011), 2767-2775 Request permission
Abstract:
We give a new approach to the study of conformal iterated function systems with arbitrary overlaps. We provide lower and upper estimates for the Hausdorff dimension of the limit sets of such systems; these are expressed in terms of the topological pressure and the function $d$, counting overlaps. In the case when the function $d$ is constant, we get an exact formula for the Hausdorff dimension. We also prove that in certain cases this formula holds if and only if the function $d$ is constant.References
Additional Information
- Eugen Mihailescu
- Affiliation: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P. O. Box 1-764, RO 014700, Bucharest, Romania
- Email: Eugen.Mihailescu@imar.ro
- Mariusz Urbański
- Affiliation: Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, Texas 76203-1430
- Email: urbanski@unt.edu
- Received by editor(s): February 9, 2010
- Received by editor(s) in revised form: July 17, 2010
- Published electronically: January 6, 2011
- Additional Notes: The research of the first author supported by CNCSIS-UEFISCSU through project PN II IDEI-1191/2008.
The research of the second author supported in part by NSF grant DMS 0700831. - Communicated by: Bryna Kra
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2767-2775
- MSC (2010): Primary 37C45, 37D35, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-2011-10704-4
- MathSciNet review: 2801617