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Given a one-parameter family of semi Riemannian metrics on an
n-dimensional manifold M, a family of time-dependent potentials and a family of trajectories connecting two points of the mechanical system defined by , we show that there are trajectories bifurcating from the trivial branch if the generalized Morse indices and are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate...
A survey of recent progress on the multiplicity and stability problems for closed geodesics on Finsler 2-spheres is given.
Using a generalization of [Pol] we present a description of complex geodesics in arbitrary complex ellipsoids.
Si studiano «combinazioni convesse complesse» per mappe olomorfe dal disco unità di in un dominio convesso limitato di uno spazio di Banach complesso , e se ne traggono conseguenze sul carattere globale della non unicità per le geodetiche complesse di .
Generalizing Cusick’s theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp neighbourhoods in negatively curved manifolds and a result of Maucourant [Mau].
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