Stability of certain planar unbounded polycycles ✩

We study the stability of a type of unbounded polycycles which appear in some planar differential equations. Each of these polycycles has hyperbolic corners, but the product of the hyperbolicity ratios of all its corners does not decide its stability. We obtain an explicit convergent integral whose sign gives the stability of the polycycle.  2002 Elsevier Science (USA). All rights reserved.