Advances in Difference Equations
Volume 2010 (2010), Article ID 324378, 18 pages
doi:10.1155/2010/324378
Research Article

Gevrey Regularity of Invariant Curves of Analytic Reversible Mappings

Dongfeng Zhang1 and Rong Cheng2

1Department of Mathematics, Southeast University, Nanjing 210096, China
2College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 19 April 2010; Revised 29 October 2010; Accepted 25 December 2010

Academic Editor: Roderick Melnik

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.

Abstract

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.