Geodesic
Existence of smooth ergodic flows on smooth manifolds
Izvestiya. Mathematics, Tome 8 (1974) no. 3, pp. 525-552 
D. V. Anosov. Existence of smooth ergodic flows on smooth manifolds. Izvestiya. Mathematics, Tome 8 (1974) no. 3, pp. 525-552. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a6/
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     author = {D. V. Anosov},
     title = {Existence of smooth ergodic flows on smooth manifolds},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that on any compact, connected, smooth manifold of dimension greater than two there exist smooth flows preserving a given measure with smooth positive density and ergodic with respect to it. (The smoothness is everywhere of infinite order.)

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