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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
In this paper we prove the existence of aGevrey family of invariant curves for analytic area preserving mappings.The Gevrey smoothness is expressedby Gevrey index. we specifically obtain the Gevreyindex of invariant curve which is related to smoothness ofarea preserving mapping and the exponent of the smalldivisors condition. Moreover, weobtain a Gevrey normal form of the area preserving mappings in aneighborhood of the union of the invariantcurves.
Keywords:Invariant curve; area preserving mapping; Gevrey index; KAM iteration