5 papers
Global center of polynomial Newton system and its non-isochronicity
Colin Christopher, Jun Zhang, Weinian Zhang
Using a new compactification (toroidal compactification) and desingularization, we obtain a complete characterization of monodromy at infinity for polynomial Newton system of arbit…
Liouvillian integrability of vector fields in higher dimensions
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider complex rational vector fields in dimension (equivalently, differential forms of degree in variables) which admit a Liouvillian first integral. Extendin…
Liouvillian integrability of three dimensional vector fields
Waleed Aziz, Colin Christopher, Chara Pantazi +1
We consider a three dimensional complex polynomial, or rational, vector field (equivalently, a two-form in three variables) which admits a Liouvillian first integral. We prove that…
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 . In view of the Pr…
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 , , is Liouvillian integrable, then it admits a first integral obtained by two successive integr…