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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| Zusammenfassung: | 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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