Finer geometric rigidity of limit sets of conformal IFS
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- by Volker Mayer and Mariusz Urbański PDF
- Proc. Amer. Math. Soc. 131 (2003), 3695-3702 Request permission
Abstract:
We consider infinite conformal iterated function systems in the phase space $\mathbb {R}^d$ with $d\ge 3$. Let $J$ be the limit set of such a system. Under a mild technical assumption, which is always satisfied if the system is finite, we prove that either the Hausdorff dimension of $J$ exceeds the topological dimension $k$ of the closure of $J$ or else the closure of $J$ is a proper compact subset of either a geometric sphere or an affine subspace of dimension $k$. A similar dichotomy holds for conformal expanding repellers.References
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Additional Information
- Volker Mayer
- Affiliation: Université de Lille I, UFR de Mathématiques, UMR 8524 du CNRS, 59655 Villeneuve d’Ascq Cedex, France
- MR Author ID: 333982
- Email: volker.mayer@univ-lille1.fr
- 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): November 18, 2001
- Published electronically: July 17, 2003
- Additional Notes: The second author was supported in part by the NSF Grant no. DMS 0100078
- Communicated by: Michael Handel
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3695-3702
- MSC (2000): Primary 37D45, 37D20, 28Exx
- DOI: https://doi.org/10.1090/S0002-9939-03-07216-2
- MathSciNet review: 1998176