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When winning
sets have full dimension
Pedro Birindiba and Katrin Gelfert
Vol. 14 (2021), No. 2, 195–207
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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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Authors |
| Pedro Birindiba | |
| Instituto de Matemática Universidade Federal do Rio de Janeiro Cidade Universitária - Ilha do Fundão Rio de Janeiro Brazil |
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| Katrin Gelfert | |
| Instituto de Matemática Universidade Federal do Rio de Janeiro Cidade Universitária - Ilha do Fundão Rio de Janeiro Brazil |
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