Copyright © 2010 Dongfeng Zhang and Rong Cheng. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 , where is the
exponent in the small divisors condition and 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.