Displaying similar documents to “Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems”

On the multiplicity of brake orbits and homoclinics in Riemannian manifolds

Roberto Giambò, Fabio Giannoni, Paolo Piccione (2005)

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

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Let M , g be a complete Riemannian manifold, Ω M an open subset whose closure is diffeomorphic to an annulus. If Ω is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in Ω ¯ = Ω Ω starting orthogonally to one connected component of Ω and arriving orthogonally onto the other one. The results given in [5] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian...