Geodesic
A representation of one-dimensional attractors of $A$-diffeomorphisms by hyperbolic homeomorphisms
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 76-87

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We give a representation for the restrictions of $A$-diffeomorphisms of closed orientable surfaces of genus $>1$ from a homotopy class containing a pseudo-Anosov diffeomorphism to all one-dimensional attractors that do not contain special pairs of boundary periodic points. The representation is given by the restriction of a hyperbolic homeomorphism to an invariant zero-dimensional set formed by the intersection of two transversal geodesic laminations. It is shown how this result can be generalized to the representation of the restrictions of $A$-diffeomorphisms defined on a closed surface of any genus to arbitrary one-dimensional attractors. 
@article{MZM_1997_62_1_a7,
     author = {V. Z. Grines},
     title = {A representation of one-dimensional attractors of $A$-diffeomorphisms by hyperbolic homeomorphisms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {76--87},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a7/}
}
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V. Z. Grines. A representation of one-dimensional attractors of $A$-diffeomorphisms by hyperbolic homeomorphisms. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 76-87. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a7/