Families of invariant tori in KAM theory: interplay of integer characteristics

TL;DR

This paper summarizes key aspects of Whitney smooth families of quasi-periodic invariant tori in KAM theory and discusses the excitation of elliptic normal modes in reversible systems, highlighting their unique features.

Contribution

It provides a concise overview of invariant tori in KAM theory and emphasizes the peculiarities of elliptic mode excitation in reversible context 2.

Findings

Summary of Whitney smooth families of invariant tori

Discussion of excitation of elliptic normal modes in reversible systems

Highlighting peculiarities in the reversible context 2

Abstract

The purpose of this brief note is twofold. First, we summarize in a very concise form the principal information on Whitney smooth families of quasi-periodic invariant tori in various contexts of KAM theory. Our second goal is to attract (via an informal discussion and a simple example) the experts' attention to the peculiarities of the so-called excitation of elliptic normal modes in the reversible context 2.