Action-angle variables and a KAM theorem for b-Poisson manifolds

TL;DR

This paper extends the action-angle theorem to b-Poisson manifolds and establishes a KAM theorem in this setting, advancing the understanding of integrable systems with singularities.

Contribution

It introduces an improved action-angle theorem for b-integrable systems on b-Poisson manifolds and proves a related KAM theorem, broadening the scope of integrable systems theory.

Findings

Proved an action-angle theorem for b-Poisson manifolds.

Established a KAM-type theorem in the b-Poisson setting.

Enhanced the understanding of integrable systems with singularities.

Abstract

In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for b-Poisson manifolds.