4 papers · 1 filter
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 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…
Poincarè-Dulac Normal Forms: Formal and Analytic Aspects
Valery G. Romanovski, Sebastian Walcher
We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincarè-Dulac normal form, and the convergence of such transformations. After…
Resnikoff silver numbers and tilings of the half-line (Dedicated to the memory of H.L.Resnikoff)
Josef F. Dorfmeister, Sebastian Walcher
Building on work by H.L.Resnikoff we consider (Resnikoff) silver numbers, which generalize the familiar golden number. By definition, a silver number is the largest positive root o…