The C0 general density theorem for geodesic flows

TL;DR

This paper proves that in the space of continuous geodesic flows on a closed Riemannian manifold, a generic set exhibits dense closed orbits, extending the understanding of geodesic dynamics.

Contribution

It establishes the C0-general density theorem for continuous geodesic flows, showing that dense closed orbits are typical in this setting.

Findings

Residual subset of flows with dense closed orbits

Extension of density results to continuous geodesic flows

Generic properties in the C0-topology for geodesic dynamics

Abstract

Given a closed Riemannian manifold, we prove the C0-general density theorem for continuous geodesic flows. More precisely, that there exists a residual (in the C0-sense) subset of the continuous geodesic flows such that, in that residual subset, the geodesic flow exhibits dense closed orbits.