A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll when they have the same minimal period. In this paper, we provide a characterization of Besse contact forms for convex contact spheres and Riemannian unit tangent bundles in terms of -equivariant spectral invariants. Furthermore, for restricted contact type hypersurfaces of symplectic vector spaces, we give a sufficient condition for the Besse property via the Ekeland–Hofer capacities.
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Viktor L. Ginzburg, Başak Z. Gürel, Marco Mazzucchelli, On the spectral characterization of Besse and Zoll Reeb flows. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 3, pp. 549–576DOI 10.1016/J.ANIHPC.2020.08.004