Quasi-periodic perturbations within the reversible context 2 in KAM theory

TL;DR

This paper extends KAM theory to quasi-periodic perturbations in reversible systems, specifically addressing the less-studied reversible context 2, and proves a new KAM-type result in this setting.

Contribution

It introduces a KAM theorem for non-autonomous reversible systems in reversible context 2, expanding the scope of invariant tori persistence results.

Findings

Proves a KAM-type theorem for reversible systems with quasi-periodic time dependence.

Provides a review of Whitney smooth families of invariant tori in Hamiltonian and reversible systems.

Addresses the gap in KAM theory for reversible context 2 systems.

Abstract

The paper consists of two sections. In Section 1, we give a short review of KAM theory with an emphasis on Whitney smooth families of invariant tori in typical Hamiltonian and reversible systems. In Section 2, we prove a KAM-type result for non-autonomous reversible systems (depending quasi-periodically on time) within the almost unexplored reversible context 2. This context 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.