4 papers
Limit cycles and invariant algebraic curves
Armengol Gasull, Paulo Santana
We give lower bounds in terms of~ for the number of limit cycles of polynomial vector fields of degree~ having any prescribed invariant algebraic curve. By applying them wh…
On the limit cycles of a quartic model for evolutionary stable strategies
Armengol Gasull, Luiz F. S. Gouveia, Paulo Santana
This paper studies the number of centers and limit cycles of the family of planar quartic polynomial vector fields that has the invariant algebraic curve The…
A note on Hilbert 16th Problem
Armengol Gasull, Paulo Santana
Let be the maximum number of limit cycles that a planar polynomial vector field of degree can have. In this paper we prove that is realizable…
On a variant of Hilbert's 16th problem
Armengol Gasull, Paulo Santana
We study the number of limit cycles that a planar polynomial vector field can have as a function of its number of monomials. We prove that the number of limit cycles increases…