Finer geometric rigidity of limit sets of conformal IFS |
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Authors: | Volker Mayer Mariusz Urbanski |
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Institution: | Université de Lille I, UFR de Mathématiques, UMR 8524 du CNRS, 59655 Villeneuve d'Ascq Cedex, France ; Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, Texas 76203-1430 |
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Abstract: | We consider infinite conformal iterated function systems in the phase space with . Let 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 exceeds the topological dimension of the closure of or else the closure of is a proper compact subset of either a geometric sphere or an affine subspace of dimension . A similar dichotomy holds for conformal expanding repellers. |
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Keywords: | |
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