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Intersection de sous-variétés lagrangiennes, fonctionnelles d’action et indice des systèmes hamiltoniens. (Intersection of Lagrangian submanifolds, action functionals and indices of Hamiltonian systems). (French) Zbl 0639.58018

Most of the advances in modern symplectic topology to a proof of Arnold’s conjectures on fixed points and Lagrangian intersections are connected beginning from Conley-Zehnder theorem with investigation of action functionals on path space in a symplectic manifold. A purely geometrical interpretation for the relative Morse index of critical points of the functional in Maslov index terms is discovered in the work and an expression of the index through conjugate points of appropriate linear Hamiltonian flows is given.
Reviewer: A.Givental’

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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