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Gevrey normal forms for nilpotent contact points of order two

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  • This paper deals with normal forms about contact points (`turning points') of nilpotent type that one frequently encounters in the study of planar slow-fast systems. In case the contact point of an analytic slow-fast vector field is of order two, we prove that the slow-fast vector field can locally be written as a slow-fast Liénard equation up to exponentially small error. The proof is based on the use of Gevrey asymptotics. Furthermore, for slow-fast jump points, we eliminate the exponentially small remainder.
    Mathematics Subject Classification: Primary: 34D14, 34A26; Secondary: 34M30, 34M60.


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