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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...

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