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math.CA2022
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^…
math.CA2022
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)\…