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| HAL : hal-00578485, version 1 |
| arXiv : 1103.4019 |
| Fiche détaillée |  Récupérer au format |
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| Minimal Ahlfors regular conformal dimension of coarse conformal dynamics on the sphere |
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| Peter Haïssinsky 1Kevin Pilgrim 2 |
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| (21/03/2011) |
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| We prove that if the Ahlfors regular conformal dimension $Q$ of a topologically cxc map on the sphere $f: S^2 \to S^2$ is realized by some metric $d$ on $S^2$, then either $Q=2$ and $f$ is topologically conjugate to a semihyperbolic rational map with Julia set equal to the whole Riemann sphere, or $Q>2$ and $f$ is topologically conjugate to a map which lifts to an affine expanding map of a torus whose differential has distinct real eigenvalues. This is an analog of a known result for Gromov hyperbolic groups with two-sphere boundary, and our methods apply to give a new proof. |
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| 1 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 2 : | Dept. of Mathematics |
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Indiana University |
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| Domaine | : | Mathématiques/Systèmes dynamiques Mathématiques/Géométrie métrique |
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| hal-00578485, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00578485 | |
| oai:hal.archives-ouvertes.fr:hal-00578485 | |
| Contributeur : Peter Haissinsky | |
| Soumis le : Lundi 21 Mars 2011, 09:59:11 | |
| Dernière modification le : Lundi 21 Mars 2011, 15:14:40 | |
