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arXiv · 2010.12893

Parrondo's paradox for homeomorphisms

Armengol Gasull·Luis Hernández-Corbato·Francisco R. Ruiz del Portal
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Abstract

We construct two planar homeomorphisms $f$ 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 greater than 2 and proves for first time the appearance of the Parrondo's dynamical paradox in odd dimensions.

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Armengol Gasull, Luis Hernández-Corbato, Francisco R. Ruiz del Portal. 2020-10-24. Parrondo's paradox for homeomorphisms. https://arxiv.org/abs/2010.12893

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