Gevrey Regularity of Invariant Curves of Analytic Reversible Mappings

Dongfeng Zhang, Rong Cheng
2010 Advances in Difference Equations  
We prove the existence of a Gevrey family of invariant curves for analytic reversible mappings under weaker nondegeneracy condition. The index of the Gevrey smoothness of the family could be any number μ > τ 2, where τ > m − 1 is the exponent in the small divisors condition and m is the order of degeneracy of the reversible mappings. Moreover, we obtain a Gevrey normal form of the reversible mappings in a neighborhood of the union of the invariant curves.
doi:10.1186/1687-1847-2010-324378 fatcat:66dhwkkc5ffrzf4b7a343luqie