45 citations · 133 across the 45 of their papers we have counts for
9 papers · 1 filter
Sturm theory with applications in geometry and classical mechanics
Vivina L. Barutello, Daniel Offin, Alessandro Portaluri +1
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…
Instability of semi-Riemannian closed geodesics
Xijun Hu, Alessandro Portaluri, Ran Yang
A celebrated result due to Poincaré affirms that a closed non-degenerate minimizing geodesic on an oriented Riemannian surface is hyperbolic. Starting from this classical theor…
Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point
Giacomo Marchesi, Alessandro Portaluri, Nils Waterstraat
We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. W…
Yet another proof of the Morse index theorem
Alessandro Portaluri, Nils Waterstraat
We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.
Bifurcation results for critical points of families of functionals
Alessandro Portaluri, Nils Waterstraat
Recently the first author studied the bifurcation of critical points of families of functionals on a Hilbert space, which are parametrised by a compact and orientable manifold havi…
Some remarks on papers: math.DG/0211091, math.DG/0306187, math.CA/0312090
A. Portaluri
This is no longer available.
A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds
Monica Musso, Jacobo Pejsachowicz, Alessandro Portaluri
Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in the presence of a potential. Our purpose here is to extend to perturbed geodesics on semi-…
On the Maslov index of symplectic paths that are not transversal to the Maslov cycle. Semi-Riemannian index theorems in the degenerate case
R. Giambo, P. Piccione, A. Portaluri
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 cas…
Spectral Flow, Maslov Index and Bifurcation of semi-Riemannian Geodesics
Paolo Piccione, Alessandro Portaluri, Daniel V. Tausk
We give a functional analytical proof of the equality between the Maslov index of a semi-Riemannian geodesic and the spectral flow of the path of self-adjoint Fredholm operators ob…