Abstract
AbstractWe show that for a generic Riemannian or reversible Finsler metric on a compact differentiable manifold M of dimension at least three all closed geodesics are simple and do not intersect each other. Using results by Contreras (Ann Math 2(172):761–808, 2010; in: Proceedings of International Congress Mathematicians (ICM 2010) Hyderabad, India, pp 1729–1739, 2011) this shows that for a generic Riemannian metric on a compact and simply-connected manifold all closed geodesics are simple and the number N(t) of geometrically distinct closed geodesics of length $$\le t$$
≤
t
grows exponentially.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
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