A note on Hilbert 16th problem

Let H(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n can have. In this paper we prove that H(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.

Detalles Bibliográficos
Autores: Gasull, Armengol|||0000-0002-1719-8231, Santana, Paulo Henrique Reis|||0000-0001-6942-351X
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:309367
Acceso en línea:https://ddd.uab.cat/record/309367
https://dx.doi.org/urn:doi:10.1090/proc/17116
Access Level:acceso abierto
Palabra clave:Hilbert 16th problem
Limit cycles
Structurally stable vector fields
Descripción
Sumario:Let H(n) be the maximum number of limit cycles that a planar polynomial vector field of degree n can have. In this paper we prove that H(n) is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite.