Geodesic
Gibbs measures for one-dimensional attractors of hyperbolic mappingss with singularities
Izvestiya. Mathematics , Tome 41 (1993) no. 3, pp. 567-580

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The author constructs and studies the properties of a $u$-Gibbs invariant measure for hyperbolic mappings with singularities, for which the unstable subspace is one-dimensional and which satisfy some regularity conditions. These conditions are satisfied by the Lorenz mapping, the Lozi mapping and the Belykh mapping among others. Various properties are proved: the denseness of periodic trajectories, topological transitivity, and convergence of the means. 
@article{IM2_1993_41_3_a7,
     author = {E. A. Sataev},
     title = {Gibbs measures for one-dimensional attractors of hyperbolic mappingss with singularities},
     journal = {Izvestiya. Mathematics },
     pages = {567--580},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1993_41_3_a7/}
}
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E. A. Sataev. Gibbs measures for one-dimensional attractors of hyperbolic mappingss with singularities. Izvestiya. Mathematics , Tome 41 (1993) no. 3, pp. 567-580. http://geodesic.mathdoc.fr/item/IM2_1993_41_3_a7/