2020/07/13 by Argyrios Christodoulou, Christodoulou, Argyrios, Natalia Jurga +1
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2007.06430
openalex publication_date 2020/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a finite set A ⊆ SL(2,ℝ) we study the dimension of the attractor KA of the iterated function system induced by the projective action of A. In particular, we generalise a recent result of Solomyak and Takahashi by showing that the Hausdorff dimension of KA is given by the minimum of 1 and the critical exponent, under the assumption that A satisfies certain discreteness conditions and a Diophantine property. Our approach combines techniques from the theories of iterated function systems and Möbius semigroups, and allows us to discuss the continuity of the Hausdorff dimension, as well as the dimension of the support of the Furstenberg measure.