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, Armengol|||0000-0002-1719-8231, Santana, Paulo Henrique Reis|||0000-0001-6942-351X
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:307723
Acceso en línea:https://ddd.uab.cat/record/307723
https://dx.doi.org/urn:doi:10.1088/1361-6544/ad8c1b
Access Level:acceso abierto
Palabra clave:Limit cycles
Hilbert 16th problem
Abelian integrals
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.