Polynomial Hamiltonian Systems with Movable Algebraic Singularities

Abstract

The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic continuation along a rectifiable curve, are at most algebraic branch points.

arXiv commentAccepted for publication in the Journal d'Analyse Mathématique; 26 pages