Geometric and spectral characterization of Zoll manifolds, invariant measures and quantum limits

Emmanuel Humbert (1) , Yannick Privat (2) , Emmanuel Trélat (3)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 IRMA - Institut de Recherche Mathématique Avancée
3 CaGE - Control And GEometry

We provide new geometric and spectral characterizations for a Riemannian manifold to be a Zoll manifold, i.e., all geodesics of which are periodic. We analyze relationships with invariant measures and quantum limits.

Mots clés: Invariant measures; Quantum limits; Zoll manifolds

Domaines: Systèmes dynamiques [math.DS]; Géométrie métrique [math.MG]; Théorie spectrale [math.SP]

Emmanuel Humbert, Yannick Privat, Emmanuel Trélat. Geometric and spectral characterization of Zoll manifolds, invariant measures and quantum limits. 2018. ⟨hal-01939709⟩