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E. Chan-López

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Preprint Aug 2026

The Bogdanov--Takens normal-form coefficients in $\mathbb{R}^n$ as directional derivatives of the characteristic invariants

Let $X$ be a vector field on an open set of $\mathbb{R}^n$ with $X(p)=0$ and Jacobian $J=DX(p)$ of rank $n-1$ having $0$ as an eigenvalue of algebraic multiplicity two. Let $q_0$ span $\ker J$ and let $e_k(A)$ denote the sum of the principal $k\times k$ minors of $A$. Under the usual hyperbolicity assumption on the tra...

E. Chan-López · 1 citation