Résumé
We present normal forms for unfoldings of regular nilpotent
contact points of slow-fast systems in the plane. The normal forms are
useful in the treatment of non-generic jump points and non-generic
turning points. For non-generic jump points, we prove a normal form of
Lienard type, while for non-generic turning points, the normal form is
of Lienard type up to exponentially small error. The techniques being
used are based on Gevrey estimates on formal power series, summation up
to exponentially small error and Gevrey version of the preparation
theorem for right equivalences.