Abstract
We present normal forms for unfoldings of nilpotent contact points of slow-fast systems in the plane. The normal forms are useful in the treatment of regular and singular contact points (including turning points). For regular contact points, we obtain a normal form of Liénard type, while for singular contact points, the normal form is of Liénard type up to exponentially small error. Our techniques are based on Gevrey estimates on formal power series and Gevrey summation. This extension of earlier results is based on a Gevrey version of Levinson’s preparation theorem.
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