Maslov indices and monodromy

2005/04/21 by H R Dullin, HR Dullin, J M Robbins +5
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:37J35 #msc:53D12 #msc:81S10 #nlin.SI

paper · pdf · doi:10.1088/0305-4470/38/24/l02

published as J. Phys. A: Math. Gen. 38 (2005) L443-L447 · 6 pages

arxiv created 2005/04/21 · openalex publication_date 2005/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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.

Citations

• On global action‐angle coordinates
• Monodromy in the resonant swing spring

Related

• Combinatorial invariant of nearly integrable Hamiltonians
• Spectral monodromy of small non-selfadjoint quantum perturbations of completely integrable Hamiltonians
• The p-cycle of Holonomic D-modules and Quantization of Exact Algebraic Lagrangians
• Tau-functions and monodromy symplectomorphisms
• Some remarks on the Maslov index