论文标题
帕伦多的同构悖论
Parrondo's paradox for homeomorphisms
论文作者
论文摘要
我们构建了两个平面同构$ f $和$ g $，该原点是全球渐近稳定的固定点，而对于$ f \ circ g $和$ g \ circ f $，原点是全球驱虫者。此外，原点仍然是由$ f $和$ g $生成的迭代功能系统的全局驱虫器，其中每个地图都以一定的概率出现。这种平面构建也扩展到大于2的任何维度，并首次证明了帕伦多在奇数上的动态悖论的出现。
We construct two planar homeomorphisms $f$ 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 greater than 2 and proves for first time the appearance of the Parrondo's dynamical paradox in odd dimensions.
