Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples

Christian Bonatti (1) , Andrey Gogolev (2) , Rafael Potrie (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Binghamton - Department of mathematical science
3 CMAT

We construct examples of robustly transitive and stably ergodic partially hyperbolic diffeomorphisms $f$ on compact 3-manifolds with fundamental groups of exponential growth such that $f^n$ is not homotopic to identity for all $n > 0$. These provide counterexamples to a classification conjecture of Pujals.

Domaines: Systèmes dynamiques [math.DS]

Christian Bonatti, Andrey Gogolev, Rafael Potrie. Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples. Inventiones Mathematicae, 2016, 206 (3), pp.801 - 836. ⟨10.1007/s00222-016-0663-7⟩. ⟨hal-01446863⟩