Canard cycle transition at a slow–fast passage through a jump point

Abstract

We introduce transitory canard cycles for slow–fast vector fields in the plane. Such cycles separate “canards without head” and “canards with head”, like for example in the Van der Pol equation. We obtain optimal upper bounds on the number of periodic orbits that can appear near the cycle under whatever condition on the related slow divergence integral I, including the challenging case I=0.