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2021 When winning sets have full dimension
Pedro Birindiba, Katrin Gelfert
Involve 14(2): 195-207 (2021). DOI: 10.2140/involve.2021.14.195

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.

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Pedro Birindiba. Katrin Gelfert. "When winning sets have full dimension." Involve 14 (2) 195 - 207, 2021. https://doi.org/10.2140/involve.2021.14.195

Information

Received: 1 July 2019; Revised: 8 July 2020; Accepted: 23 December 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/involve.2021.14.195

Subjects:
Primary: 28A78, 28A80, 37C45, 91A44

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 2 • 2021
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