Applied Maths Seminar: Halburd -- Movable Algebraic Singularities of Solutions of ODEs

Rod Halburd, Department of Mathematics, University College London 

A class of second-order rational ordinary differential equations admitting certain
families of formal algebraic series solutions is considered.  For all solutions of these
equations, it is shown that any movable singularity that can be reached by analytic
continuation along a finite length curve is an algebraic branch point.  The existence of
these formal series expansions is straightforward to determine for any given equation in
the class considered.