Seifert manifolds admitting partially hyperbolic diffeomorphisms

Andy Hammerlindl (1) , Rafael Potrie (2) , Mario Shannon (2, 3)

1 School of Mathematical Sciences [Clayton]
2 CMAT - Centro de Matemática [Montevideo]
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.

Mots clés: Partially hyperbolic diffeomorphisms; Seifert spaces

Domaines: Systèmes dynamiques [math.DS]; Topologie générale [math.GN]

Andy Hammerlindl, Rafael Potrie, Mario Shannon. Seifert manifolds admitting partially hyperbolic diffeomorphisms. Journal of modern dynamics, 2018, 12, pp.193-222. ⟨10.3934/jmd.2018008⟩. ⟨hal-01900109⟩