Darboux theory of integrability for real polynomial vector fields on Sⁿ

This is a survey on the Darboux theory of integrability for polynomial vector fields, first in Rⁿ and second in the n-dimensional sphere Sⁿ. We also provide new results about the maximum number of invariant parallels and meridians that a polynomial vector field X on Sⁿ can have in function of its de...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Murza, Adrian|||0000-0001-9521-5052
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:199352
Acceso en línea:https://ddd.uab.cat/record/199352
https://dx.doi.org/urn:doi:10.1080/14689367.2017.1420141
Access Level:acceso abierto
Palabra clave:Darboux integrability theory
Invariant meridian
Invariant parallel
N-dimensional spheres
Descripción
Sumario:This is a survey on the Darboux theory of integrability for polynomial vector fields, first in Rⁿ and second in the n-dimensional sphere Sⁿ. We also provide new results about the maximum number of invariant parallels and meridians that a polynomial vector field X on Sⁿ can have in function of its degree. These results in some sense extend the known result on the maximum number of hyperplanes that a polynomial vector field Y in Rⁿ can have in function of the degree of Y.