Conformality for a robust class of non-conformal attractors
In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and establish a convergence property for them, analogue to a differentiability property. As an application of this converge...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
4 Feb 2019
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| In: |
Arxiv
Year: 2019, Pages: 1-56 |
| Online Access: | Verlag, Volltext: http://arxiv.org/abs/1902.01303
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| Author Notes: | Beatrice Pozzetti, Andrés Sambarino, and Anna Wienhard |
| Summary: | In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and establish a convergence property for them, analogue to a differentiability property. As an application of this convergence, we prove that the Hausdorff dimension of the limit set of a hyperconvex representation is equal to a suitably chosen critical exponent. In the appendix, in collaboration with M. Bridgeman, we extend a classical result on the Hessian of the Hausdorff dimension on purely imaginary directions. |
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| Item Description: | Gesehen am 11.02.2019 |
| Physical Description: | Online Resource |