Conformality for a robust class of non-conformal attractors

Author:

Pozzetti Maria Beatrice1,Sambarino Andrés2,Wienhard Anna3

Affiliation:

1. Mathematisches Institut , Ruprecht-Karls Universität Heidelberg , Im Neuenheimer Feld 205, 69120 Heidelberg , Germany

2. Sorbonne Université , IMJ-PRG (CNRS UMR 7586) , 4 place Jussieu, 75005 Paris , France

3. Mathematisches Institut , Ruprecht-Karls Universität Heidelberg , Im Neuenheimer Feld 205, 69120 Heidelberg , Germany ; and HITS gGmbH, Heidelberg Institute for Theoretical Studies,Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany

Abstract

Abstract 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.

Funder

Agence Nationale de la Recherche

Deutsche Forschungsgemeinschaft

European Research Council

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference45 articles.

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3. J. Bochi and N. Gourmelon, Some characterizations of domination, Math. Z. 263 (2009), no. 1, 221–231.

4. J. Bochi, R. Potrie and A. Sambarino, Anosov representations and dominated splittings, J. Eur. Math. Soc. (JEMS) 21 (2019), no. 11, 3343–3414.

5. M. Bourdon, Structure conforme au bord et flot géodésique d’un CAT ⁢ ( - 1 ) {\rm CAT}(-1) -espace, Enseign. Math. (2) 41 (1995), no. 1–2, 63–102.

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