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Parrondo's paradox for homoeomorphisms

Published online by Cambridge University Press:  16 June 2021

A. Gasull
Affiliation:
Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Barcelona, Spain Centre de Recerca Matemàtica, Edifici Cc, Campus de Bellaterra, 08193 Cerdanyola del Vallès, Barcelona, Spain (gasull@mat.uab.cat)
L. Hernández-Corbato
Affiliation:
Departamento de Álgebra, Geometría y Topología Universidad Complutense de Madrid and Instituto de Ciencias Matematicas CSIC–UAM–UCM–UC3M, Madrid, Spain (luishcorbato@mat.ucm.es)
F. R. Ruiz del Portal
Affiliation:
Departamento de Álgebra, Geometría y Topología Universidad Complutense de Madrid, 28040 Madrid, Spain (rrportal@ucm.es)

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.

Type
Research Article
Copyright
Copyright © The Author(s) 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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