Let (M, g) be a complete Riemannian manifold, and let Ω ⊂ M be an open subset whose closure is homeomorphic to a disk or to an annulus. In this note we discuss some multiplicity results for orthogonal geodesic chords in Ω, namely geodesics in Ω starting from and arriving orthogonally to the boundary of Ω. This kind of problems has applications to multiplicity results for brake orbits and homoclinics, via Maupertuis principle.
Multiplicity results for orthogonal geodesic chords and applications
GIAMBO', Roberto;GIANNONI, Fabio;
2014-01-01
Abstract
Let (M, g) be a complete Riemannian manifold, and let Ω ⊂ M be an open subset whose closure is homeomorphic to a disk or to an annulus. In this note we discuss some multiplicity results for orthogonal geodesic chords in Ω, namely geodesics in Ω starting from and arriving orthogonally to the boundary of Ω. This kind of problems has applications to multiplicity results for brake orbits and homoclinics, via Maupertuis principle.File in questo prodotto:
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