Conformality for a robust class of non-conformal attractors

• Verfasst von: Pozzetti, Maria Beatrice [VerfasserIn]
• Verfasst von: Sambarino, Andrés [VerfasserIn]
• Verfasst von: Wienhard, Anna [VerfasserIn]
• Titel: Conformality for a robust class of non-conformal attractors
• Verf.angabe: Beatrice Pozzetti, Andrés Sambarino, and Anna Wienhard
• E-Jahr: 2019
• Jahr: 4 Feb 2019
• Umfang: 56 S.
• Teil: year:2019
• Teil: elocationid:1902.01303
• Teil: pages:1-56
• Teil: extent:56
• Fussnoten: Gesehen am 11.02.2019
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2019
• Band/Heft Quelle: (2019), Artikel-ID 1902.01303, Seite 1-56
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Mathematics - Differential Geometry
• Sach-SW: Mathematics - Dynamical Systems
• Sach-SW: Mathematics - Group Theory
• K10plus-PPN: 158744657X

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.