Vol. 14, No. 2, 2021

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When winning sets have full dimension

Pedro Birindiba and Katrin Gelfert

Vol. 14 (2021), No. 2, 195–207
Abstract

We investigate when sets which are winning in the sense of Schmidt games have full Hausdorff dimension. The classical result by Schmidt asserts that winning sets for games played in Euclidean spaces have full dimension. We recover this type of result for games played on attractors of contracting iterated function systems: either on a complete metric space with semiconformal contractions or on n and an iterated function system of C1 conformal maps with Hölder continuous derivative.

Keywords
Schmidt game, Hausdorff dimension, attractor of iterated function system, Ahlfors regularity, doubling measure
Mathematical Subject Classification 2010
Primary: 91A44, 28A80, 28A78, 37C45
Milestones
Received: 1 July 2019
Revised: 8 July 2020
Accepted: 23 December 2020
Published: 6 April 2021

Communicated by Kenneth S. Berenhaut
Authors
Pedro Birindiba
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Cidade Universitária - Ilha do Fundão
Rio de Janeiro
Brazil
Katrin Gelfert
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Cidade Universitária - Ilha do Fundão
Rio de Janeiro
Brazil