On the equidistribution of closed geodesics and geodesic nets

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We show that given a closed n n -manifold M M , for a Baire-generic set of Riemannian metrics g g on M M there exists a sequence of closed geodesics that are equidistributed in M M if n = 2 n=2 ; and an equidistributed sequence of embedded stationary geodesic nets if n = 3 n=3 . One of the main tools that we use is the Weyl law for the volume spectrum for 1 1 -cycles, proved by Liokumovich, Marques, and Neves [Ann. of Math. (2) 187 (2018), pp. 933–961] for n = 2 n=2 and by Guth and Liokumovich [Preprint, arXiv:2202.11805, 2022] for n = 3 n=3 . We show that our proof of the equidistribution of stationary geodesic nets can be generalized for any dimension n ≥ 2 n\geq 2 provided the Weyl Law for 1 1 -cycles in n n -manifolds holds.