Related papers: On the Maslov-type index for general paths of symp…
The Conley-Zehnder index associates an integer to any continuous path of symplectic matrices starting from the identity and ending at a matrix which does not admit 1 as an eigenvalue. We give new ways to compute this index. Robbin and…
We propose a topological theory of the Maslov index for lagrangian and symplectic paths based on a minimal system of axioms. We recover, as particular cases, the Hoermander and the Robbin-Salomon indices.
We give here a self contained and elementary introduction to the Conley-Zehnder index for a path of symplectic matrices. We start from the definition of the index as the degree of a map into the circle for a path starting at the identity…
In this paper, we explicitly express the local Maslov index by a Maslov index in finite dimensional case without symplectic reduction. Then we calculate the Maslov index for the path of pairs of Lagrangian subspaces in triangular form. In…
In this paper we present the theory of oscillation numbers and dual oscillation numbers for continuous Lagrangian paths in $\mathbb{R}^{2n}$. Our main results include a connection of the oscillation numbers of the given Lagrangian path with…
In this paper, we prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space. Then we give a direct proof of iteration formulae for the Maslov-type…
In this note it is shown that the Maslov Index for pairs of Lagrangian Paths as introduced by Cappell, Lee and Miller appears by parallel transporting elements of (a certain complex line-subbundle of) the symplectic spinorbundle over…
The aim of this paper is to give an explicit formula for the calculation of the Gutzwiller--Maslov index of a Hamiltonian periodic orbit. We identify the index appearing in Gutzwiller's trace formula with a non-trivial extension of the…
It is shown that there is a generalization of the Conley-Zehnder index for periodic trajectories of a classical Hamiltonian system $(Q, \omega, H)$ from the case $Q = T^*R^n$ to arbitrary symplectic manifolds. As it turns out, it is…
We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the case of a real-analytic path having possibly non transversal…
It is proved that the Maslov index naturally arises in the framework of PDEs geometry. The characterization of PDE solutions by means of Maslov index is given. With this respect, Maslov index for Lagrangian submanifolds is given on the…
We construct a homotopy invariant index for pathes in the set of invertible tripotents in a JB*-triple that satisfy a Fredholm type condition with respect to a fixed invertible tripotent. That index generalizes the Maslov index in the…
Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley--Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We…
In this paper, we give the definition of Maslov-type index of the discrete Hamiltonian system, and obtain the relation of Morse index and Maslov-type index of the discrete Hamiltonian system which is a generalization of case $\omega=1$ in…
These are the notes of rather informal lectures given by the first co-author in UPMC, Paris, in January 2017. Practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows to…
We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the…
We address the problem of computing the Maslov index for large linear symplectic systems on the real line. The Maslov index measures the signed intersections (with a given reference plane) of a path of Lagrangian planes. The natural chart…
Maslov indices in periodic-orbit theory are investigated using phase space path integral. Based on the observation that the Maslov index is the multi-valued function of the monodromy matrix, we introduce a generalized monodromy matrix in…
We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying (weak) symplectic structures. Assuming vanishing index, we obtain intrinsically a continuously varying splitting of the total…
We define the Maslov index of a loop tangent to the characteristic foliation of a coisotropic submanifold as the mean Conley--Zehnder index of a path in the group of linear symplectic transformations, incorporating the "rotation" of the…