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. 
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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/

[1] Nielsen J., “Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. I; II”, Acta Math., 50 (1927), 189–358 ; Acta Math., 53 (1929), 1–76 | DOI | DOI

[2] Thurston W., “On geometry and dynamics of diffeomorphisms of surfaces”, Bull. Amer. Math. Soc., 19:2 (1988), 417–431 | DOI | MR | Zbl

[3] Aranson S. Kh., Grines V. Z., “Topologicheskaya klassifikatsiya kaskadov na zamknutykh dvumernykh mnogoobraziyakh”, UMN, 45:4 (1990), 3–32 | MR | Zbl

[4] Aranson S. Kh., Grines V. Z., “Gl. 3. Kaskady na poverkhnostyakh”, Dinamicheskie sistemy s giperbolicheskim povedeniem, Itogi nauki i tekhn. Sovrem. probl. matem. Fundament. napravleniya, 66, 1991, 148–187 | MR | Zbl

[5] Aranson S. Kh., Grines V. Z., “Gomeomorfizmy s minimalnoi entropiei na dvumernykh mnogoobraziyakh”, UMN, 36:2 (1981), 175–176 | MR | Zbl

[6] Aranson S. Kh., Grines V. Z., Dinamicheskie sistemy s minimalnoi entropiei na dvumernykh mnogoobraziyakh, Dep. VINITI No 3181–V80, GGU im. N. I. Lobachevskogo, Gorkii, 1980

[7] Plykin R. V., “Istochniki i stoki $A$-diffeomorfizmov poverkhnostei”, Matem. sb., 94:2 (1974), 243–264 | MR | Zbl

[8] Grines V. Z., “O topologicheskoi sopryazhennosti diffeomorfizmov dvumernogo mnogoobraziya na odnomernykh orientiruemykh bazisnykh mnozhestvakh, I”, Tr. MMO, 32, URSS, M., 1975, 35–61 | MR

[9] Plykin R. V., “O geometrii giperbolicheskikh attraktorov gladkikh kaskadov”, UMN, 39:6 (1984), 75–113 | MR | Zbl

[10] Zhirov A. Yu., Plykin R. V., “Sootvetstvie mezhdu odnomernymi giperbolicheskimi attraktorami diffeomorfizmov poverkhnostei i obobschennymi psevdoanosovskimi diffeomorfizmami”, Matem. zametki, 58:1 (1995), 149–152 | MR | Zbl

[11] Grines V. Z., “O topologicheskoi sopryazhennosti diffeomorfizmov dvumernogo mnogoobraziya na odnomernykh orientiruemykh bazisnykh mnozhestvakh, II”, Tr. MMO, 34, URSS, M., 1977, 243–252 | MR | Zbl

[12] Grines V. Z., “Structural stability and the asymptotic behaviour of invariant manifolds of $A$-diffeomorphisms of surfaces”, J. Dynam. Control Systems, 3:1 (1997), 91–110 | DOI | MR | Zbl

[13] Grines V. Z., Kalai Kh. Kh., Topologicheskaya klassifikatsiya bazisnykh mnozhestv bez par sopryazhennykh tochek $A$-diffeomorfizmov na poverkhnostyakh, Dep. VINITI No. 1137–V88, GGU im. N. I. Lobachevskogo, Gorkii, 1988

[14] Nielsen J., “Surface transformation classes of algebraically finite type”, Det. Kgl. Dansk Videnskaternes Selskab. Math.–Phys. Meddelerser, 21 (1944), 1–89