Stably ergodic diffeomorphisms which are not partially hyperbolic

DDIC

Keywords: Stable ergodicity | SRB measures | Dominated decomposition

We show stable ergodicity of a class of conservative diffeomorphisms of $\mathbb{T}^n$ which do not have any hyperbolic invariant subbundle. Moreover, the uniqueness of SRB (Sinai-Ruelle-Bowen) measure for non-conservative $C^1$ perturbations of such diffeomorphisms is verified. This class strictly contains non-partially hyperbolic robustly transitive diffeomorphisms constructed by Bonatti-Viana and so we answer the question posed by them on stable ergodicity of such systems.

Anexos:

• int2.ps