Conformality for a robust class of non-conformal attractors

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. 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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Submitted on : Sunday, December 8, 2019 - 12:53:06 PM
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  • HAL Id : hal-02391752, version 1
  • ARXIV : 1902.01303

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Beatrice Pozzetti, Andres Sambarino, Anna Wienhard. Conformality for a robust class of non-conformal attractors. 2019. ⟨hal-02391752⟩

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