#### 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 ${ℝ}^{n}$ and an iterated function system of ${C}^{1}$ 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