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- W2138492720 abstract "Using the ideas of Keller, Maslov introduced in the mid-1960's an index for Lagrangian loops, whose definition was clarified by Arnold. Leray extended Arnold results by defining an index depending on two paths of Lagrangian planes with transversal endpoints. We show that the combinatorial and topological properties of Leray's index suffice to recover all Lagrangian and symplectic intersection indices commonly used in symplectic geometry and its applications to Hamiltonian and quantum mechanics. As a by-product we obtain a new simple formula for the Hörmander index, and a definition of the Conley–Zehnder index for symplectic paths with arbitrary endpoints. Our definition leads to a formula for the Conley–Zehnder index of a product of two paths. Utilisant les idées de Keller, Maslov introduisit au milieu des années 1960 un indice pour les lacets lagrangiens ; Arnold clarifia par la suite la définition de Maslov. Leray étendit les résultats de Arnold en définissant un indice dépendant de deux chemins lagrangiens dont les extrêmités sont transversales. Nous montrons que les propriétés combinatoires et topologiques qui caractérisent l'indice de Leray sont suffisantes pour retrouver tous les indices d'intersection lagrangiens et symplectiques communément utilisés en géométrie symplectique, et ses applications à la mécanique hamiltonienne et quantique. Nous obtenons en outre une nouvelle formule simple pour l'indice de Hörmander, ainsi qu'une définition de l'indice de Conley–Zehnder pour les chemins symplectiques sans condition de transversalité. Notre définition permet en outre de démontrer une formula pour l'indice de Conley–Zehnder du produit des deux chemins symplectiques." @default.
- W2138492720 created "2016-06-24" @default.
- W2138492720 creator A5050598781 @default.
- W2138492720 date "2009-06-01" @default.
- W2138492720 modified "2023-09-25" @default.
- W2138492720 title "On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths" @default.
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- W2138492720 doi "https://doi.org/10.1016/j.matpur.2009.04.004" @default.
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