Parrondo´s paradox for homeomorphisms

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Gasull, A. and Hernández Corbato, Luis and Ruiz del Portal, Francisco R. (2021) Parrondo´s paradox for homeomorphisms. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics . ISSN 0308-2105

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Official URL: https://doi.org/10.1017/prm.2021.28



Abstract

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.


Item Type:Article
Uncontrolled Keywords:Fixed points; Local and global asymptotic stability; Parrondo’s dynamical paradox; Random dynamical system
Subjects:Sciences > Mathematics
Sciences > Mathematics > Geometry
ID Code:73470
Deposited On:06 Jul 2022 10:46
Last Modified:06 Jul 2022 12:05

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