Geodesic
Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets
Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 862-909

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We consider orientation-preserving $A$-diffeomorphisms of orientable surfaces of genus greater than one with a one-dimensional spaciously situated perfect attractor. We show that the topological classification of restrictions of diffeomorphisms to such basic sets can be reduced to that of pseudo-Anosov homeomorphisms with a distinguished set of saddles. In particular, we prove a result announced by Zhirov and Plykin, which gives a topological classification of the $A$-diffeomorphisms of the surfaces under discussion under the additional assumption that the non-wandering set consists of a one-dimensional spaciously situated attractor and zero-dimensional sources.
Keywords: one-dimensional basic set, perfect attractor, spaciously situated set.
Mots-clés : axiom $A$ 
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     title = {Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets},
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V. Z. Grines; E. D. Kurenkov. Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets. Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 862-909. http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a2/