A NOTE ON HILBERT 16TH PROBLEM

Author(s)

Gasull, Armengol ; Santana, Paulo

• Document type: Journal article
• Source: Proceedings of the American Mathematical Society; v. 153, n. 2, p. 9-pg., 2024-12-17.

Abstract

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. (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: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants
• 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