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Parrondo's paradox for homoeomorphisms
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2021-06-16 , DOI: 10.1017/prm.2021.28 A. Gasull , L. Hernández-Corbato , F. R. Ruiz del Portal
中文翻译:
Parrondo 的同胚悖论
更新日期:2021-06-16
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2021-06-16 , DOI: 10.1017/prm.2021.28 A. Gasull , L. Hernández-Corbato , F. R. Ruiz del Portal
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 $>$2 and proves for first time the appearance of the dynamical Parrondo's paradox in odd dimensions.
中文翻译:
Parrondo 的同胚悖论
我们构造了两个平面同胚$f$和$g$,它们的原点是一个全局渐近稳定不动点,而对于$f\circ g$和$g\circ f$,原点是一个全局排斥器。此外,原点仍然是由$f$和$g$生成的迭代函数系统的全局排斥器,其中每个映射以一定的概率出现。这种平面结构也扩展到任何维度$>$ 2,并首次证明了动力帕隆多悖论在奇数维度中的出现。