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Abstract
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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
and an iterated
function system of
conformal maps with Hölder continuous derivative.
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Keywords
Schmidt game, Hausdorff dimension, attractor of iterated
function system, Ahlfors regularity, doubling measure
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Mathematical Subject Classification 2010
Primary: 91A44, 28A80, 28A78, 37C45
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Milestones
Received: 1 July 2019
Revised: 8 July 2020
Accepted: 23 December 2020
Published: 6 April 2021
Communicated by Kenneth S. Berenhaut
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