2020/10/24 by Armengol Gasull, Gasull, Armengol, Luis Hernández–Corbato +4 · 1 citation
Mathematics · Physics and Astronomy · #37C25 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37C25
paper · pdf · doi:10.48550/arxiv.2010.12893
arxiv created 2020/10/24 · openalex publication_date 2020/10/24 · arxiv updated 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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.