Geodesic
Markov splitting for U-flows in three-dimensional manifolds
Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 693-704.

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A construction is presented of Markov splitting for U-flows in three-dimensional manifolds, having everywhere-dense bands layered transversely. 
@article{MZM_1969_6_6_a5,
     author = {M. E. Ratner},
     title = {Markov splitting for {U-flows} in three-dimensional manifolds},
     journal = {Matemati\v{c}eskie zametki},
     pages = {693--704},
     publisher = {mathdoc},
     volume = {6},
     number = {6},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a5/}
}
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M. E. Ratner. Markov splitting for U-flows in three-dimensional manifolds. Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 693-704. http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a5/