Small solutions of nonlinear differential equations near branching points (Q647875)

The authors consider scalar implicit ordinary differential equations of arbitrary order in the neighbourhood of a branching point and construct parametric families of small solutions. They first analyse the Newton diagrams of homogeneous components of the equation and then use the results for a reduction to a first-order system of equations with a regular singularity. In addition, they describe a technique for determining the asymptotic behaviour of their solution family.