The center bundle of a conservative partially hyperbolic diffeomorphism $f$ is called robustly non-hyperbolic if any conservative diffeomorphism which is $C^1$-close to $f$ has non-hyperbolic center bundle. In this paper, we prove that stable ergodicity is $C^1$-dense among conservative partially hyperbolic systems with robust non-hyperbolic center.
On the Stable Ergodicity of Berger-Carrasco's example
Stable ergodicity of dominated systems
Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1d-center bundle
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