Abstract
We give a representation for the restrictions ofA-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 ofA-diffeomorphisms defined on a closed surface of any genus to arbitrary one-dimensional attractors.
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Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 76–87, July, 1997.
Translated by V. E. Nazaikinskii
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Grines, V.Z. A representation of one-dimensional attractors ofA-diffeomorphisms by hyperbolic homeomorphisms. Math Notes 62, 64–73 (1997). https://doi.org/10.1007/BF02356065
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DOI: https://doi.org/10.1007/BF02356065