MORSE INDEX AND BIFURCATION OF p-GEODESICS ON SEMI RIEMANNIAN MANIFOLDS
TLDR
In this article, it was shown that there are trajectories bifurcating from the trivial branch σλ if the generalized Morse indices µ(σa )a nd µ (σb) are different.Abstract:
Given a one-parameter family {gλ : λ ∈ (a, b)} of semi Riemannian metrics on an n- dimensional manifold M , a family of time-dependent potentials {Vλ : λ ∈ (a, b)} and a family {σλ : λ ∈ (a, b)} of trajectories connecting two points of the mechanical system defined by (gλ ,V λ), we show that there are trajectories bifurcating from the trivial branch σλ if the generalized Morse indices µ(σa )a nd µ(σb) 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 Schoenberg type.read more
Citations
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Index theory for heteroclinic orbits of Hamiltonian systems
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Bifurcation of critical points for continuous families of C 2 functionals of Fredholm type
TL;DR: In this article, it was shown that the nonvanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of points along the branch.
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An index theory for asymptotic motions under singular potentials
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