KAM theory for lower dimensional tori within the reversible context 2

TL;DR

This paper extends KAM theory to lower-dimensional invariant tori within the reversible context 2, where the fixed point manifold's dimension varies, using Moser's modifying terms theorem to establish persistence results.

Contribution

It generalizes the persistence of invariant tori in reversible context 2 for arbitrary fixed point manifold dimensions, beyond the previously studied case where dim Fix G = 0.

Findings

Established KAM-type persistence results for arbitrary dim Fix G

Extended the theory beyond the special case dim Fix G = 0

Utilized Moser's modifying terms theorem for the proof

Abstract

The reversible context 2 in KAM theory refers to the situation where dim Fix G < (1/2) codim T, here Fix G is the fixed point manifold of the reversing involution G and T is the invariant torus one deals with. Up to now, the persistence of invariant tori in the reversible context 2 has been only explored in the extreme particular case where dim Fix G = 0 [M. B. Sevryuk, Regul. Chaotic Dyn. 16 (2011), no. 1-2, 24-38]. We obtain a KAM-type result for the reversible context 2 in the general situation where the dimension of Fix G is arbitrary. As in the case where dim Fix G = 0, the main technical tool is J. Moser's modifying terms theorem of 1967.