Maslov Indices and Monodromy

TL;DR

This paper establishes a relationship between Maslov indices and monodromy in Liouville-integrable Hamiltonian systems, showing the Maslov index vector as an eigenvector of the monodromy matrix with eigenvalue 1, leading to restrictions on monodromy.

Contribution

It proves that in such systems, the Maslov index vector is an eigenvector of the monodromy matrix with eigenvalue 1, revealing new constraints on monodromy matrices.

Findings

Maslov index vector is an eigenvector of monodromy matrix

Restrictions on monodromy matrix derived from Maslov indices

Results apply to Liouville-integrable Hamiltonian systems

Abstract

We prove that for a Hamiltonian system on a cotangent bundle that is Liouville-integrable and has monodromy the vector of Maslov indices is an eigenvector of the monodromy matrix with eigenvalue 1. As a corollary the resulting restrictions on the monodromy matrix are derived.