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Published online: 2011-03-06
Denseness of ergodicity for a class of volume-preserving flowsMário Bessa and Jorge Rocha (1) Universidade do Porto, Portugal
(2) Universidade do Porto, Portugal
We consider the class of $C^1$ partially hyperbolic volume-preserving flows with one-dimensional central direction endowed with the $C^1$-Whitney topology. We prove that, within this class, any flow can be approximated by an ergodic $C^2$ volume-preserving flow and so, as a consequence, ergodicity is dense.
Keywords: Dominated splitting, partial hyperbolicity, volume-preserving flows, Lyapunov exponents, stable ergodicity
Bessa Mário, Rocha Jorge: Denseness of ergodicity for a class of volume-preserving flows. Port. Math. 68 (2011), 1-17. doi: 10.4171/PM/1878