Conformality for a robust class of non-conformal attractors

Beatrice Pozzetti , Andres Sambarino (1, 2) , Anna Wienhard (3)

1 CNRS - Centre National de la Recherche Scientifique
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 Universität Heidelberg [Heidelberg] = Heidelberg University

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.

Domaines: Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]

Beatrice Pozzetti, Andres Sambarino, Anna Wienhard. Conformality for a robust class of non-conformal attractors. J. fur die reine und ange. Math, 2020, ⟨10.1515/crelle-2020-0029⟩. ⟨hal-02391752v2⟩