Gasull, A.Hernández Corbato, LuisRuiz del Portal, Francisco R.2023-06-172023-06-172021-06-160308-210510.1017/prm.2021.28https://hdl.handle.net/20.500.14352/7231We 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.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttps://doi.org/10.1017/prm.2021.28open access514Fixed pointsLocal and global asymptotic stabilityParrondo’s dynamical paradoxRandom dynamical systemMatemáticas (Matemáticas)Geometría12 Matemáticas1204 Geometría