Rigidity of cotangent lifts and integrable systems

TL;DR

This paper extends Palais's theorem on the rigidity of compact group actions to cotangent lifts and applies it to demonstrate rigidity in integrable systems on symplectic manifolds, including those with degenerate singularities.

Contribution

It generalizes a classical rigidity theorem to cotangent lifts and applies this to prove rigidity results for integrable systems with singularities.

Findings

Rigidity of cotangent lifts established

Rigidity results for integrable systems proven

Includes systems with degenerate singularities

Abstract

In this article we generalize a theorem by Palais on the rigidity of compact group actions to cotangent lifts. We use this result to prove rigidity for integrable systems on symplectic manifolds including sytems with degenerate singularities which are invariant under a torus action.