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).
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Elementary spectral invariants simplify embedded contact homology spectral invariants for contact three-manifolds and can be used to prove some results on periodic orbits of Reeb vector fields, with the remaining results requiring the full ECH invariants.
citing papers explorer
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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).
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Elementary spectral invariants and three-dimensional Reeb dynamics
Elementary spectral invariants simplify embedded contact homology spectral invariants for contact three-manifolds and can be used to prove some results on periodic orbits of Reeb vector fields, with the remaining results requiring the full ECH invariants.