Computation of the Maslov index and the spectral flow via partial signatures
@article{Giamb2004ComputationOT, title={Computation of the Maslov index and the spectral flow via partial signatures}, author={Roberto Giamb{\`o} and Paolo Piccione and Alessandro Portaluri}, journal={Comptes Rendus Mathematique}, year={2004}, volume={338}, pages={397-402} }
32 Citations
On the Maslov index of symplectic paths that are not transversal to the Maslov cycle. Semi-Riemannian index theorems in the degenerate case
- Mathematics
- 2003
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…
ON THE MASLOV INDEX OF LAGRANGIAN PATHS THAT ARE NOT TRANSVERSAL TO THE MASLOV CYCLE. SEMI-RIEMANNIAN INDEX THEOREMS IN THE DEGENERATE CASE
- Mathematics
- 2003
The Maslov index of a Lagrangian path, under a certain trans versality assumption, is given by an algebraic count of the intersection s f the path with a subvariety of the Lagrangian Grassmannian…
Spectral Flow, Maslov Index and Bifurcation of Semi-Riemannian Geodesics
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We give a functional analytical proof of the equalitybetween the Maslov index of a semi-Riemannian geodesicand the spectral flow of the path of self-adjointFredholm operators obtained from the index…
On a formula for the spectral flow and its applications
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- 2008
We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms…
Iteration of closed geodesics in stationary Lorentzian manifolds
- Mathematics
- 2007
Following the lines of Bott in (Commun Pure Appl Math 9:171–206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a…
Instability of semi-Riemannian closed geodesics
- MathematicsNonlinearity
- 2019
A celebrated result due to Poincare affirms that a closed non-degenerate minimizing geodesic $\gamma$ on an oriented Riemannian surface is hyperbolic. Starting from this classical theorem, our first…
Sturm theory with applications in geometry and classical mechanics
- Mathematics
- 2020
Classical Sturm non-oscillation and comparison theorems as well as the Sturm theorem on zeros for solutions of second order differential equations have a natural symplectic version, since they…
Linear instability for periodic orbits of non-autonomous Lagrangian systems
- Mathematics
- 2019
Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the…
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