On the spectral characterization of Besse and Zoll Reeb flows

Viktor L. Ginzburg , Basak Z. Gurel , Marco Mazzucchelli (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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 $S^1$-equivariant spectral invariants. Furthermore, for restricted contact type hypersurfaces of symplectic Euclidean spaces, we give a sufficient condition for the Besse property via the Ekeland-Hofer capacities.

Domaines: Mathématiques [math]; Géométrie symplectique [math.SG]; Systèmes dynamiques [math.DS]

Viktor L. Ginzburg, Basak Z. Gurel, Marco Mazzucchelli. On the spectral characterization of Besse and Zoll Reeb flows. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2020, ⟨10.1016/j.anihpc.2020.08.004⟩. ⟨ensl-02352680⟩