On a variant of Hilbert's 16th problem

Author(s)

Gasull, Armengol ; Santana, Paulo

• Document type: Journal article
• Source: Nonlinearity; v. 37, n. 12, p. 15-pg., 2024-12-02.

Abstract

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. (AU)

• FAPESP's process: 22/14353-1 - Study of polycycles with applications in game theory
• Grantee: Paulo Henrique Reis Santana
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 21/01799-9 - The study of vector fields with applications at game theory
• Grantee: Paulo Henrique Reis Santana
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants