We use nonsmooth critical point theory and the theory of geodesics with obstacle to show a multiplicity result about orthogonal geodesic chords in a Riemannian manifold (with boundary) which is homeomorphic to an N-disk. This applies to brake orbits in a potential well of a natural Hamiltonian system, providing a further step towards the proof of a celebrated conjecture by Seifert (Math Z 51:197–216, 1948).
Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles
Giambò, Roberto;Giannoni, Fabio;
2018-01-01
Abstract
We use nonsmooth critical point theory and the theory of geodesics with obstacle to show a multiplicity result about orthogonal geodesic chords in a Riemannian manifold (with boundary) which is homeomorphic to an N-disk. This applies to brake orbits in a potential well of a natural Hamiltonian system, providing a further step towards the proof of a celebrated conjecture by Seifert (Math Z 51:197–216, 1948).File in questo prodotto:
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Calc. Var., 2018, 57, p. 117.pdf
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Descrizione: Articolo Pre-print da arXiv.org, math, arXiv:1807.00887v1
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