Equidistributed Closed Geodesics on Closed Finsler and Riemannian Surfaces

Abstract: In this paper, we establish the existence of an equidistributed sequence of nondegenerate closed geodesics for generic Finsler, symmetric Finsler and Riemannian metrics on every closed surface. The proof relies on the volume property of embedded contact homology, established by Cristofaro-Gardiner, Hutchings and Ramos, along with specific local variational constructions and transversality arguments. Our approach is motivated by Irie's equidistribution result in [19] for three-dimensional Reeb flows and the analogous result presented by Marques, Neves and Song [27] for embedded minimal hypersurfaces.