Computation of the Maslov index and the spectral flow via partial signatures.

DOI10.1016/j.crma.2004.01.004zbMath1039.37006OpenAlexW2139263325MaRDI QIDQ1426628

Paolo Piccione, Alessandro Portaluri, Roberto Giambò

Publication date: 15 March 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.01.004

zbMATH Keywords

bifurcationgeodesicsMorse indexspectral flowMaslov indexpartial signaturessemi-Riemannian version

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Lagrangian submanifolds; Maslov index (53D12) Index theory for dynamical systems, Morse-Conley indices (37B30) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Spectral flows (58J30) Sub-Riemannian geometry (53C17)

Related Items (20)

Extensions of symmetric operators that are invariant under scaling and applications to indicial operators ⋮ Spectral stability, spectral flow and circular relative equilibria for the Newtonian \(n\)-body problem ⋮ Hörmander's index and oscillation theory ⋮ Hamiltonian Spectral Flows, the Maslov Index, and the Stability of Standing Waves in the Nonlinear Schrodinger Equation ⋮ An index theory for asymptotic motions under singular potentials ⋮ Index theory for heteroclinic orbits of Hamiltonian systems ⋮ Signature and spectral flow of \(J\)-unitary \(\mathbb S^1\)-Fredholm operators ⋮ Generalized symplectic Cayley transforms and a higher order formula for the Conley-Zehnder index of symplectic paths ⋮ Keplerian orbits through the Conley-Zehnder index ⋮ Sturm theory with applications in geometry and classical mechanics ⋮ Linear instability for periodic orbits of non-autonomous Lagrangian systems ⋮ Iteration of closed geodesics in stationary Lorentzian manifolds ⋮ On a formula for the spectral flow and its applications ⋮ Linear instability of relative equilibria for \(n\)-body problems in the plane ⋮ A generalization of Yoshida-Nicolaescu theorem using partial signatures ⋮ A bifurcation result for semi-Riemannian trajectories of the Lorentz force equation ⋮ Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory ⋮ Spectral flow and iteration of closed semi-Riemannian geodesics ⋮ A dihedral Bott-type iteration formula and stability of symmetric periodic orbits ⋮ Instability of semi-Riemannian closed geodesics

Cites Work

• Unnamed Item
• The Weil representation, Maslov index and theta series
• On the Morse index in variational calculus
• The Maslov index: A functional analytical definition and the spectral flow formula
• The Maslov index for paths
• The Morse index theorem in semi-Riemannian geometry
• Generalized Jordan chains and two bifurcation theorems of Krasnoselskii
• Self-Adjoint Fredholm Operators And Spectral Flow
• The spectral flow of the odd signature operator and higher Massey products
• Jumps of the eta-invariant. (With an appendix by Shmuel Weinberger: Rationality of \(\rho\)-invariants)

This page was built for publication: Computation of the Maslov index and the spectral flow via partial signatures.