Herman's approach to quasi-periodic perturbations in the reversible KAM context 2

TL;DR

This paper extends Herman's method to establish Whitney smooth families of invariant tori in quasi-periodic non-autonomous reversible systems within the less-studied context 2 of KAM theory, where fixed point manifolds are relatively small.

Contribution

It adapts Herman's approach to the reversible KAM context 2, providing new results on the existence and smoothness of invariant tori in these systems.

Findings

Existence of Whitney smooth families of invariant tori

Extension of Herman's method to reversible context 2

Applicable to systems with small fixed point manifolds

Abstract

We revisit non-autonomous systems depending quasi-periodically in time within the reversible context 2 of KAM theory and obtain Whitney smooth families of invariant tori in such systems via Herman's method. The reversible KAM context 2 refers to the situation where the dimension of the fixed point manifold of the reversing involution is less than half the codimension of the invariant torus in question.