On the measure of KAM tori in two degrees of freedom

TL;DR

This paper discusses a conjecture regarding the exponentially small measure of the set of non-KAM tori in analytic systems with two degrees of freedom, contributing to the understanding of stability regions in Hamiltonian dynamics.

Contribution

It analyzes a conjecture by Arnold, Kozlov, and Neishtadt on the measure of non-torus sets, providing insights into the size of stability regions in such systems.

Findings

Supports the conjecture of exponentially small measure of non-torus sets

Provides theoretical insights into KAM tori in two degrees of freedom

Enhances understanding of stability in Hamiltonian systems

Abstract

A conjecture of Arnold, Kozlov and Neishtadt on the exponentially small measure of the non-torus set in analytic systems with two degrees of freedom is discussed.