Morse index and bifurcation of p-geodesics on semi riemannian manifolds
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 598-621.

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 points along a trajectory using an explicit computation of the Morse index in the case of locally symmetric spaces and a comparison principle of Morse Schöenberg type.

DOI : 10.1051/cocv:2007037
Classification : 58E10, 37J45, 53C22, 58J30
Mots clés : generalized Morse index, semi-riemannian manifolds, perturbed geodesic, bifurcation
Musso, Monica  ; Pejsachowicz, Jacobo  ; Portaluri, Alessandro 1

1 Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-900, São Paulo, SP Brazil; Current address: Dipartimento di Matematica, Politecnico di Torino, Italy
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     title = {Morse index and bifurcation of $p$-geodesics on semi riemannian manifolds},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {598--621},
     publisher = {EDP-Sciences},
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Musso, Monica; Pejsachowicz, Jacobo; Portaluri, Alessandro. Morse index and bifurcation of $p$-geodesics on semi riemannian manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 598-621. doi : 10.1051/cocv:2007037. http://www.numdam.org/articles/10.1051/cocv:2007037/

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