We give a functional analytical proof of the equality between the Maslov index of a semi-Riemannian geodesic and the spectral ow of the path of self-adjoint Fredholm operators obtained from the index… (More)

We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The… (More)

We prove an extension of the Index Theorem for Morse–Sturm s ystems of the form−V ′′ + RV = 0, whereR is symmetric with respect to a (non positive) symmetric bilinear form, and thus the correspond… (More)

We investigate the problem of the stability of the number of conjugate or focal points (counted with multiplicity) along a semi-Riemannian geodesic γ. For a Riemannian or a nonspacelike Lorentzian… (More)

Conway and Kochen have presented a “free will theorem” [4, 6] which they claim shows that “if indeed we humans have free will, then [so do] elementary particles.” In a more precise fashion, they… (More)

Introduction It has become evident through many mathematical theories of our century that Geometry and Topology offer very powerful tools in the study of qualitative and also quantitative properties… (More)

The origins of this topic is a famous paper by Einstein, Rosen and Podolsky (EPR) in 1935; its title was Can Quantum-Mechanical Description of Physical Reality be Considered Complete? They considered… (More)

Helfer in [6] was the first to produce an example of a spacelike Lorentzian geodesic with a continuum of conjugate points. In this paper we show the following result: given an interval [a, b] of IR… (More)

We consider aHamiltonian setup(M, ω, H, L,Γ,P), where(M, ω) is a symplectic manifold,L is a distribution of Lagrangian subspaces in M, P a Lagrangian submanifold ofM, H is a smooth time dependent… (More)

We prove a version of the Morse Index Theorem for periodic geodesics in a stationary Lorentzian manifold. This theorem relates the index of a suitable restriction of the second variation of the… (More)