Colin Christopher

collaborators

3 papers

nlin.SI2025

Liouvillian integrability of vector fields in higher dimensions

Waleed Aziz, Colin Christopher, Chara Pantazi +1

We consider complex rational vector fields in dimension $n > 2$ (equivalently, differential forms of degree $n - 1$ in $n$ variables) which admit a Liouvillian first integral. Extendin…

math.RA2025

Liouvillian integrability of rational vector fields: The case of algebraic extensions

Colin Christopher, Chara Pantazi, Sebastian Walcher

As shown in a previous paper, whenever a rational vector field on $C^{n}$ , $n > 2$ , is Liouvillian integrable, then it admits a first integral obtained by two successive integr…

math.DS2024

On elementary integrability of rational vector fields

Colin Christopher, Sebastian Walcher

We consider complex rational vector fields that admit a first integral whose logarithmic derivative lies in a finite extension of the rational function field $K$ . In view of the Pr…