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Conformality for a robust class of non-conformal attractors

  • Maria Beatrice Pozzetti , Andrés Sambarino EMAIL logo and Anna Wienhard

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.

Award Identifier / Grant number: ANR-16-CE40-0025

Award Identifier / Grant number: 338644254

Award Identifier / Grant number: 614733

Funding statement: Andrés Sambarino was partially financed by ANR DynGeo ANR-16-CE40-0025. Beatrice Pozzetti and Anna Wienhard acknowledge funding by the Deutsche Forschungsgemeinschaft Project number 338644254 within the Priority Program SPP 2026 “Geometry at Infinity”. Anna Wienhard acknowledges funding by the European Research Council under ERC-Consolidator grant 614733, and by the Klaus-Tschira-Foundation.

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Received: 2019-04-12
Revised: 2020-03-28
Published Online: 2020-10-08
Published in Print: 2021-05-01

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