3 citations · 6 across the 12 of their papers we have counts for
14 papers
On the cyclicity of Kolmogorov polycycles
David Marín, Jordi Villadelprat
In this paper we study planar polynomial Kolmogorov's differential systems \[ X_μ\quad\sist{xf(x,y;μ),}{yg(x,y;μ),} \] with the parameter varying in an open subset $Λ\subset\R^…
The criticality of reversible quadratic centers at the outer boundary of its period annulus
David Marín, Jordi Villadelprat
This paper deals with the period function of the reversible quadratic centers \begin{equation*} X_{\np}=-y(1-x)\partial_x+(x+Dx^2+Fy^2)\partial_y, \end{equation*} where $\np=(D,F)\…
Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles: Coefficient properties
David Marín, Jordi Villadelprat
We consider a family of planar vector fields having a hyperbolic saddle and we study the Dulac map and the Dulac t…
Geometry of certain foliations on the complex projective plane
Samir Bedrouni, David Marín
Let be an integer. The set of foliations of degree on the complex projective plane can be identified with a Zariski's open set of a projective space of…
Convex foliations of degree 4 on the complex projective plane
Samir Bedrouni, David Marín
We show that up to automorphisms of there are homogeneous convex foliations of degree four on Using this result, we give…
Classification of foliations of degree three on with a flat Legendre transform
Samir Bedrouni, David Marín
The set of foliations of degree three on the complex projective plane can be identified with a Zariski's open set of a projective space of dimension on which a…