On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths

DOI10.1016/j.matpur.2009.04.004zbMath1179.53080OpenAlexW2138492720MaRDI QIDQ1029162

Maurice A. De Gosson

Publication date: 9 July 2009

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2009.04.004

zbMATH Keywords

Maslov indexConley-Zehnder indexsymplectic pathsLagrangian paths

Mathematics Subject Classification ID

Global theory of symplectic and contact manifolds (53D35) Lagrangian submanifolds; Maslov index (53D12)

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Relative phase shifts for metaplectic isotopies acting on mixed Gaussian states ⋮ The Maslov index and some applications to dispersion relations in curved space times ⋮ A Bangert-Hingston theorem for starshaped hypersurfaces ⋮ Sturm intersection theory for periodic Jacobi matrices and linear Hamiltonian systems ⋮ The Maslov Index in Symplectic Banach Spaces ⋮ Gutzwiller's semiclassical trace formula and Maslov-type index theory for symplectic paths ⋮ Compact exact Lagrangian intersections in cotangent bundles via sheaf quantization ⋮ Hörmander index in finite-dimensional case ⋮ Symplectic covariance properties for Shubin and Born–Jordan pseudo-differential operators

Cites Work

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• Fredholm-Lagrangian-Grassmannian and the Maslov index
• A primitive of the generalized Maslov cocycle
• Generalized symplectic Cayley transforms and a higher order formula for the Conley-Zehnder index of symplectic paths
• On a product formula for the Conley-Zehnder index of symplectic paths and its applications
• The Weil representation, Maslov index and theta series
• Euler and Maslov cocycles
• On the Morse index in variational calculus
• Invariants homotopiques attachés aux fibres symplectiques
• Semiclassical principal symbols and Gutzwiller's trace formula
• Trace formulas and the Conley-Zehnder index
• The Maslov index for paths
• The generalized Maslov index
• The Maslov index revisited
• Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
• The Morse index theorem in semi-Riemannian geometry
• The structure of \(q\)-symplectic geometry
• Properties of pseudo-holomorphic curves in symplectisations. II: Embedding controls and algebraic invariants
• Symplectic geometry and quantum mechanics
• Maslov index and Novikov-Wall theorem
• Multiplicity and stability of closed geodesics on Finsler 2-spheres
• Non-additivity of the signature
• Fourier integral operators. I
• On the Weyl representation of metaplectic operators
• Extension of the Conley-Zehnder index, a product formula, and an application to the Weyl representation of metaplectic operators
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• On the maslov index
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations