Gibbs measures for one-dimensional attractors of hyperbolic mappingss with singularities

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.