Parrondo´s paradox for homeomorphisms

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 m...

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Detalles Bibliográficos
Autores: Gasull, A., Hernández Corbato, Luis, Ruiz del Portal, Francisco R.
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/7231
Acceso en línea:https://hdl.handle.net/20.500.14352/7231
Access Level:acceso abierto
Palabra clave:514
Fixed points
Local and global asymptotic stability
Parrondo’s dynamical paradox
Random dynamical system
Matemáticas (Matemáticas)
Geometría
12 Matemáticas
1204 Geometría
Descripción
Sumario: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.