Parrondo's paradox for homoeomorphisms

Parrondo's paradox for homoeomorphisms

We construct two planar homoeomorphisms f and g for which the origin is a globally asymptotically stable fixed point whereas for f∘g and g∘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...

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Hauptverfasser: Gasull, Armengol, Hernández-Corbato, L, Ruiz Del Portal, F. R
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Dynamical Parrondo's paradox
Fixed points
Local and global asymptotic stability
Random dynamical systems
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Hernández-Corbato, L
Ruiz Del Portal, F. R
description We construct two planar homoeomorphisms f and g for which the origin is a globally asymptotically stable fixed point whereas for f∘g and g∘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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subjects Dynamical Parrondo's paradox
Fixed points
Local and global asymptotic stability
Random dynamical systems
title Parrondo's paradox for homoeomorphisms
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