Vanishing set of inverse Jacobi multipliers and attractor/repeller sets

In this paper, we study conditions under which the zero-set of the inverse Jacobi multiplier of a smooth vector field contains its attractor/repeller compact sets. The work generalizes previous results focusing on sink singularities, orbitally asymptotic limit cycles, and monodromic attractor graphi...

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Detalles Bibliográficos
Autores: García, Isaac|||0000-0001-6982-9632, Giné, Jaume|||0000-0001-7109-2553, Llibre, Jaume|||0000-0002-9511-5999, Maza, Susanna|||0000-0001-9488-5644
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:236646
Acceso en línea:https://ddd.uab.cat/record/236646
https://dx.doi.org/urn:doi:10.1063/5.0020360
Access Level:acceso abierto
Palabra clave:Attractor set
Repulsor set
Jacobi multiplier
Vector fields
Flows
Ordinary differential equations
Descripción
Sumario:In this paper, we study conditions under which the zero-set of the inverse Jacobi multiplier of a smooth vector field contains its attractor/repeller compact sets. The work generalizes previous results focusing on sink singularities, orbitally asymptotic limit cycles, and monodromic attractor graphics. Taking different flows on the torus and the sphere as canonical examples of attractor/repeller sets with different topologies, several examples are constructed illustrating the results presented.