We consider the class of partially hyperbolic volume-preserving flows with one-dimensional central direction endowed with the -Whitney topology. We prove that, within this class, any flow can be approximated by an ergodic volume-preserving flow and so, as a consequence, ergodicity is dense.
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Mário Bessa, Jorge Rocha, Denseness of ergodicity for a class of volume-preserving flows. Port. Math. 68 (2011), no. 1, pp. 1–17DOI 10.4171/PM/1878