Under a non-nilpotency condition in free loop space homology with respect to the Chas-Sullivan product, the number of simple Reeb orbits on star-shaped hypersurfaces grows at least like T/log(T).
Remark on non-contractible closed geodesics and ho- motopy groups.arXiv preprint arXiv:2307.13877
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On the growth rate of Reeb orbit on star-shaped hypersurfaces
Under a non-nilpotency condition in free loop space homology with respect to the Chas-Sullivan product, the number of simple Reeb orbits on star-shaped hypersurfaces grows at least like T/log(T).