Work

Hausdorff dimension, diverging Schottky representations and the infinite dimensional hyperbolic space

Year: 2024

Type: preprint

Abstract: One of our main goals in this paper is to understand the behavior of limit sets of a diverging sequence of Schottky groups in the group of isometries of the N-dimensional hyperbolic space. This leads us to a generalization of a classical theorem of Bowen on variations of Hausdorff dimension of limit sets; and to a method of transforming a diverging sequence of Schottky groups into an almost converging sequence in the group of isometries of the infinite dimensional hyperbolic space. Our results apply in particular to an example of McMullen and generalize a previous work by Mehmeti and Dang.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2410.10266

Authors: Guilloux, Antonin, Courtois, Gilles

Institutions: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Université Paris Diderot, OURAGAN: Outils de Résolution Algébriques pour la Géométrie et ses Applications

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Hilbert geometries over any valued field

OpenAlex ID: W4403407060

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