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dynamical parrondo's paradox

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Parrondo's paradox for homoeomorphisms
Part of
- Random dynamical systems
- Smooth dynamical systems: general theory
A. Gasull, L. Hernández-Corbato, F. R. Ruiz del Portal
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 4 / August 2022

Published online by Cambridge University Press:

16 June 2021, pp. 817-825

Print publication:

August 2022
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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.