4 problems

Consider the polynomial system denoted by (gs), its Bautin ideal $B$, and the associated parameter-space vector field denoted by (Vvfsh). Bautin-variety invariance conjecture. The…

Let ${\bf W}$ be a component of the integrability variety ${\bf V}(B)$ of the system under consideration. Let $\mathcal A|_{\bf W}$ denote the restriction to ${\bf W}$ of the opera…

Consider the $1:-1$ resonant polynomial system … Let $I_S$ be its Sibirsky ideal and let $B$ be the Bautin ideal, with ${\bf V}(I_S)$ and ${\bf V}(B)$ their varieties. Sibirsky ide…

Let $P_n(x,y)$ and $Q_n(x,y)$ be polynomials of degree $n$, defining the planar polynomial system … An invariant line is a straight line preserved by the flow of this system. Ye's…