On a variant of Hilbert's 16th problem

We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m <= 10.

Detalles Bibliográficos
Autores: Gasull, A., Santana, P.
Tipo de recurso: artículo
Fecha de publicación:2024
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:2072/480067
Acceso en línea:http://hdl.handle.net/2072/480067
Access Level:acceso abierto
Palabra clave:Limit cycles
Hilbert 16th problem
Abelian integrals
51
Descripción
Sumario:We study the number of limit cycles that a planar polynomial vector field can have as a function of its number m of monomials. We prove that the number of limit cycles increases at least quadratically with m and we provide good lower bounds for m <= 10.