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Parrondo's paradox for homoeomorphisms
Published online by Cambridge University Press: 16 June 2021
Abstract
We construct two planar homoeomorphisms $f$ and $g$ for which the origin is a globally asymptotically stable fixed point whereas for $f \circ g$ and $g \circ f$ the origin is a global repeller. Furthermore, the origin remains a global repeller for the iterated function system generated by $f$ and $g$ where each of the maps appears with a certain probability. This planar construction is also extended to any dimension $>$2 and proves for first time the appearance of the dynamical Parrondo's paradox in odd dimensions.
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 4 , August 2022 , pp. 817 - 825
- Copyright
- Copyright © The Author(s) 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh