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.
Pozzetti M.B., Sambarino A., Wienhard A. (2021). Conformality for a robust class of non-conformal attractors. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 2021(774), 1-51 [10.1515/crelle-2020-0029].
Conformality for a robust class of non-conformal attractors
Pozzetti M. B.;
2021
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.| File | Dimensione | Formato | |
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