Geodesic
The topology of basis sets for Smale diffeomorphisms
Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 297-307 
R. V. Plykin. The topology of basis sets for Smale diffeomorphisms. Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 297-307. http://geodesic.mathdoc.fr/item/SM_1971_13_2_a6/
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     title = {The topology of basis sets for {Smale} diffeomorphisms},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Diffeomorphisms of a closed surface are considered which satisfy Smale's axiom $A$ and an acyclicity condition. It is shown that if one of its basis sets is one-dimensional, then there is also a zero-dimensional source or sink. As a preliminary, some auxiliary propositions of general character are established concerning sources and sinks of diffeomorphisms satisfying the axiom and the condition above. Bibliography: 10 titles.

[1] D. V. Anosov, Geodezicheskie potoki na zamknutykh mnogoobraziyakh otritsatelnoi krivizny, Trudy Matem. in-ta im. V. A. Steklova, XC, 1967

[2] D. V. Anosov, Ob odnom klasse invariantnykh mnozhestv gladkikh dinamicheskikh sistem, Mezhdunar. simpozium po nelineinym kolebaniyam. Tezisy dokladov, Kiev, 1969

[3] M. A. Avez, “Topologie des diffeomorphismes D'Anosov qui possedent un invariant integral”, C. R. Acad. Sci., 265 (1967), 503–510

[4] W. Hurewicz, “Uber den sogenannten Produksatz der Dimensionstheorie”, Math. Ann., 102 (1930), 305–312 | DOI | MR

[5] V. Gurevich, G. Volmen, Teoriya razmernosti, IL, Moskva, 1948

[6] V. I. Pupko, “O nesamoperesekayuschikhsya krivykh na zamknutykh poverkhnostyakh”, DAN SSSR, 177:2 (1967), 272–274 | MR | Zbl

[7] Ya. G. Sinai, “Markovskie razbieniya i $Y$-diffeomorfizmy”, Funkts. analiz, 2:1 (1968), 64–89 | MR | Zbl

[8] S. Smeil, “Differentsiruemye dinamicheskie sistemy”, Uspekhi matem. nauk, XXV:1(151) (1970), 113–185 | MR

[9] S. Smeil, “Teorema $\Omega$-ustoichivosti”, Matematika, 13:2 (1969), 161–169

[10] R. V. Plykin, “Diffeomorfizmy Smeila na zamknutykh poverkhnostyakh”, Uspekhi matem. nauk, XXIV:2(146) (1969), 231–232 | MR