Quasi-periodic motions in generic nearly-integrable mechanical systems

TL;DR

This paper discusses the typical behavior of nearly-integrable mechanical systems with generic analytic potentials, focusing on the existence and measure of invariant tori, extending previous theoretical results.

Contribution

It presents new results on the measure of Lagrangian invariant tori in generic nearly-integrable systems, building upon and briefly discussing a theorem from prior work.

Findings

Results on the measure of invariant tori in generic systems

Extension of previous theoretical theorems

Insights into the typical dynamics of nearly-integrable systems

Abstract

In this note we present and briefly discuss results, which include as a particular case the theorem announced in [L. Biasco, and L. Chierchia. On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), 1-10], concerning the typical behaviour of nearly-integrable mechanical systems with generic analytic potentials.