2 problems

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The Bautin-variety invariance conjecture for polynomial vector fields
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…
Conjectureopenbautin-ideal integrability polynomial-vector-fieldsarXiv posted 2 days ago
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The Sibirsky ideal component conjecture
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…
Conjectureopenbautin-ideal integrability polynomial-vector-fieldsarXiv posted 2 days ago

The Bautin-variety invariance conjecture for polynomial vector fields