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Parrondo´s paradox for homeomorphisms

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2021

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Cambridge University Press
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We construct two planar homeomorphisms 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 greater than 2 and proves for first time the appearance of the Parrondo’s dynamical paradox in odd dimensions.

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