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2005 Orthogonal geodesic chords, brake orbits and homoclinic orbits in Riemannian manifolds
Roberto Giambò, Fabio Giannoni, Paolo Piccione
Adv. Differential Equations 10(8): 931-960 (2005).


The study of solutions with fixed energy of certain classes of Lagrangian (or Hamiltonian) systems is reduced, via the classical Maupertuis--Jacobi variational principle, to the study of geodesics in Riemannian manifolds. We are interested in investigating the problem of existence of brake orbits and homoclinics, in which case the Maupertuis--Jacobi principle produces a Riemannian manifold with boundary and with metric degenerating in a nontrivial way on the boundary. In this paper we use the classical Maupertuis--Jacobi principle to show how to remove the degeneration of the metric on the boundary, and we prove in full generality how the brake orbit and the homoclinic multiplicity problem can be reduced to the study of multiplicity of orthogonal geodesic chords in a manifold with regular and strongly concave boundary.


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Roberto Giambò. Fabio Giannoni. Paolo Piccione. "Orthogonal geodesic chords, brake orbits and homoclinic orbits in Riemannian manifolds." Adv. Differential Equations 10 (8) 931 - 960, 2005.


Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1118.37031
MathSciNet: MR2150871

Primary: 37J45
Secondary: 58E10

Rights: Copyright © 2005 Khayyam Publishing, Inc.


Vol.10 • No. 8 • 2005
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