3 problems

Let $N\geq 3$, let $A_j(t)$, for $j=2,3,\ldots,N-1$, be polynomial functions, and consider the differential equation … A solution is a center at the origin if nearby solutions have…

Component-count conjecture. The variety $X_{\infty}$ has exactly $1$ component of codimension $5$, exactly $2$ components of codimension $6$, exactly $4$ components of codimension…

Component-count conjecture. The number of reduced components of the center variety in degree $3$ is $1$ in codimension $5$, $2$ in codimension $6$, $4$ in codimension $7$, $4$ in c…