English

Parrondo's paradox for homeomorphisms

Dynamical Systems 2020-10-27 v1

Abstract

We construct two planar homeomorphisms ff and gg for which the origin is a globally asymptotically stable fixed point whereas for fgf \circ g and gfg \circ f the origin is a global repeller. Furthermore, the origin remains a global repeller for the iterated function system generated by ff and gg 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.

Keywords

Cite

@article{arxiv.2010.12893,
  title  = {Parrondo's paradox for homeomorphisms},
  author = {Armengol Gasull and Luis Hernández-Corbato and Francisco R. Ruiz del Portal},
  journal= {arXiv preprint arXiv:2010.12893},
  year   = {2020}
}
R2 v1 2026-06-23T19:37:00.695Z