2 citations · 3 across the 10 of their papers we have counts for
10 papers
The cyclicity of hyperbolic hemicycles
David Marín, Jordi Villadelprat
We consider families of planar polynomial vector fields of degree and study the cyclicity of a type of unbounded polycycle~ called hemicycle. Compactified to the Poincaré di…
The period of the limit cycle bifurcating from a persistent polycycle
David Marín, Lucas Queiroz, Jordi Villadelprat
We consider smooth families of planar polynomial vector fields , where is an open subset of , for which there is a hyperbolic polycycle that…
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)\…
Non-bifurcation of critical periods from semi-hyperbolic polycycles of quadratic centers
David Marín, Mariana Saavedra, Jordi Villadelprat
In this paper we consider the unfolding of saddle-node \[ X= \frac{1}{xU_a(x,y)}\Big(x(x^μ-\varepsilon)\partial_x-V_a(x)y\partial_y\Big), \] parametrized by with…
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…