Closing geodesics in C1 topology

Ludovic Rifford (1, 2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 APICS - Analysis and Problems of Inverse type in Control and Signal processing

Given a closed Riemannian manifold, we show how to close an orbit of the geodesic flow by a small perturbation of the metric in the C1 topology.

Domaines: Systèmes dynamiques [math.DS]; Géométrie métrique [math.MG]; Optimisation et contrôle [math.OC]

Ludovic Rifford. Closing geodesics in C1 topology. Journal of Differential Geometry, 2012, 91 (3), pp.361. ⟨hal-00923324⟩