Noncommutative integrability and action-angle variables in contact geometry

TL;DR

This paper introduces a new concept of noncommutative integrability within contact geometry, expanding the theoretical framework for understanding integrable systems in this geometric setting.

Contribution

It proposes a novel definition of noncommutative integrability tailored for contact geometry, bridging a gap in the existing mathematical theory.

Findings

Defines noncommutative integrability in contact geometry

Establishes foundational properties of the new framework

Lays groundwork for future research in contact integrable systems

Abstract

We introduce a notion of the noncommutative integrability within a framework of contact geometry.