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Morse index and bifurcation of p-geodesics on semi Riemannian manifolds

Monica Musso, Jacobo Pejsachowicz, Alessandro Portaluri (2007)

ESAIM: Control, Optimisation and Calculus of Variations

Given a one-parameter family { g λ : λ ∈ [ a , b ] } of semi Riemannian metrics on an n-dimensional manifold M, a family of time-dependent potentials { V λ : λ ∈ [ a , b ] } and a family { σ λ : λ ∈ [ a , b ] } of trajectories connecting two points of the mechanical system defined by ( g λ , V λ ) , we show that there are trajectories bifurcating from the trivial branch σ λ if the generalized Morse indices μ ( σ a ) and μ ( σ b ) 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...

On non-Uniqueness of Complex Geodesies in Convex Bounded Domains

Graziano Gentili (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano «combinazioni convesse complesse» per mappe olomorfe dal disco unità di ℂ in un dominio convesso limitato D di uno spazio di Banach complesso E , e se ne traggono conseguenze sul carattere globale della non unicità per le geodetiche complesse di D .

On the closedness of approximation spectra

Jouni Parkkonen, Frédéric Paulin (2009)

Journal de Théorie des Nombres de Bordeaux

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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