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...
| Autores: | , , |
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| 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 |
| 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. |
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