Author

E. Chan-López

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Preprint Sep 2026

Newton geometry of Bogdanov-Takens degeneracies in integrable dilatonic models: invariant divisors and boundary multiplicity

The Kantowski--Sachs interior of Grumiller's two-dimensional dilaton gravity model reduces to $\dot H=\tfrac12(\Lambda-3H^2-u^2)+Qu$, $\dot u=-Hu$, where $H$ is the expansion rate of the orbit two-spheres, $u$ their inverse areal radius, and $Q$ is minus twice the Rindler acceleration. For $Q\neq0$ it has two distinct...

E. Chan-López, A. Martín-Ruiz, J. M. Paulin Fuentes · 0 citations

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