Simple Flows on Tori with Uncommon Chaos

We consider a family of simple flows in tori that display chaotic behavior in a wide sense. But these flows do not have homoclinic nor heteroclinic orbits. They have only a fixed point which is of parabolic type. However, the dynamics returns infinitely many times near the fixed point due to quasi-p...

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Detalles Bibliográficos
Autor: Simó, C.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/530714
Acceso en línea:http://hdl.handle.net/2072/530714
Access Level:acceso abierto
Palabra clave:Matemàtiques
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Descripción
Sumario:We consider a family of simple flows in tori that display chaotic behavior in a wide sense. But these flows do not have homoclinic nor heteroclinic orbits. They have only a fixed point which is of parabolic type. However, the dynamics returns infinitely many times near the fixed point due to quasi-periodicity. A preliminary example is given for maps introduced in a paper containing many examples of strange attractors in [6]. Recently, a family of maps similar to the flows considered here was studied in [9]. In the present paper we consider the case of 2D tori and the extension to tori of arbitrary finite dimension. Some other facts about exceptional frequencies and behavior around parabolic fixed points are also included.