2024/10/14 by Antonin Guilloux, Guilloux, Antonin, Gilles Courtois +1
Computer Science · Mathematics · #Digital Image Processing Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2410.10266
openalex publication_date 2024/10/14 · openalex created_date 2024/10/15 · openalex updated_date 2026/07/28
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.