@article{SM_2002_193_6_a4,
author = {E. V. Zhuzhoma and V. S. Medvedev},
title = {On non-orientable two-dimensional basic sets on~3-manifolds},
journal = {Sbornik. Mathematics},
pages = {869--888},
year = {2002},
volume = {193},
number = {6},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2002_193_6_a4/}
}
E. V. Zhuzhoma; V. S. Medvedev. On non-orientable two-dimensional basic sets on 3-manifolds. Sbornik. Mathematics, Tome 193 (2002) no. 6, pp. 869-888. http://geodesic.mathdoc.fr/item/SM_2002_193_6_a4/
[1] Anosov D. V., Geodezicheskie potoki na zamknutykh rimanovykh mnogoobraziyakh otritsatelnoi krivizny, Tr. MIAN, 90, Nauka, M., 1967 | MR
[2] Anosov D. V., “Ob odnom klasse invariantnykh mnozhestv gladkikh dinamicheskikh sistem”, Kachestvennye metody, Trudy pyatoi mezhdunarodnoi konferentsii po nelineinym kolebaniyam, T. 2 (In-t matematiki AN USSR), Naukova Dumka, Kiev, 1970, 39–45
[3] Anosov D. V., “Grubye sistemy”, Tr. MIAN, 169, Nauka, M., 1985, 59–93 | MR
[4] Anosov D. V., Solodov V. V., “Giperbolicheskie mnozhestva”, Dinamicheskie sistemy – 9, Itogi nauki i tekhniki. Sovrem. probl. matem. Fundam. napr., 66, VINITI, M., 1991, 12–99 | MR | Zbl
[5] Franks J., “Anosov diffeomorphisms”, Global analysis, Proc. Sympos. Pure Math., 14, 1970, 61–94 ; Gladkie dinamicheskie sistemy, Mir, M., 1977, 32–86 | MR | MR
[6] Newhouse S., “On codimension one Anosov diffeomorphisms”, Amer. J. Math., 92:3 (1970), 761–770 ; Gladkie dinamicheskie sistemy, Mir, M., 1977, 87–98 | DOI | MR | Zbl
[7] Smale S., “Differentiable dynamical systems”, Bull. Amer. Math. Soc. (N.S.), 73:1 (1967), 741–817 ; UMN, 25 (1970), 113–185 | MR
[8] Kollmer H., “On hyperbolic attractors of codimension one”, Lecture Notes in Math., 597, 1977, 330–334 | MR | Zbl
[9] Plante J., “The homology class of an expanded invariant manifolds”, Lecture Notes in Math., 468, 1975, 251–256 | MR | Zbl
[10] Grines V. Z., “O topologicheskoi sopryazhennosti diffeomorfizmov dvumernogo mnogoobraziya na odnomernykh orientiruemykh bazisnykh mnozhestvakh. I; II”, Tr. MMO, 32, URSS, M., 1975, 35–60 ; Тр. ММО, 34, УРСС, М., 1977, 234–252 | MR | Zbl | MR
[11] Plykin R. V., “Istochniki i stoki $A$-diffeomorfizmov poverkhnostei”, Matem. sb., 94 (1974), 243–264 | MR | Zbl
[12] Grines V. Z., Kalai Kh. Kh., “Diffeomorfizmy dvumernykh mnogoobrazii s prostorno raspolozhennymi bazisnymi mnozhestvami”, UMN, 40:1 (1985), 189–190 | MR | Zbl
[13] Plykin R. V., “O suschestvovanii prityagivayuschikh (ottalkivayuschikh) periodicheskikh tochek $A$-diffeomorfizmov proektivnoi ploskosti i butylki Kleina”, UMN, 32:3 (1977), 179 | MR | Zbl
[14] Plykin R. V., “O giperbolicheskikh attraktorakh diffeomorfizmov”, UMN, 35:3 (1980), 94–104 | MR | Zbl
[15] Plykin R. V., “O geometrii giperbolicheskikh attraktorov gladkikh kaskadov”, UMN, 39:6 (1984), 75–113 | MR | Zbl
[16] Zhirov A. Yu., “Perechislenie giperbolicheskikh attraktorov na orientiruemykh poverkhnostyakh i primeneniya k psevdoanosovskim gomeomorfizmam”, Dokl. RAN, 330:6 (1993), 683–686 | MR | Zbl
[17] Zhirov A. Yu., “Giperbolicheskie attraktory diffeomorfizmov orientiruemykh poverkhnostei. I: Kodirovanie, klassifikatsiya i nakrytiya”, Matem. sb., 185:6 (1994), 3–50 ; “Гиперболические аттракторы диффеоморфизмов ориентируемых поверхностей. II: Перечисление и применение к псевдоаносовским диффеоморфизмам”, Матем. сб., 185:9 (1994), 29–80 ; “Гиперболические аттракторы диффеоморфизмов ориентируемых поверхностей. III: Алгоритм классификации”, Матем. сб., 186:2 (1995), 59–82 | MR | Zbl | Zbl | MR | Zbl
[18] Plykin R. V., “O topologii bazisnykh mnozhestv diffeomorfizmov Smeila”, Matem. sb., 84 (1971), 301–312 | MR | Zbl
[19] Katok A., Hasselblatt B., Introduction to the modern theory of dynamical systems, Encyclopedia Math. Appl., 54, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl
[20] Aranson S. Kh., Grines V. Z., “Kaskady na povepkhnostyakh”, Dinamicheskie sistemy – 9, Itogi nauki i tekhniki. Sovrem. probl. matem. Fundam. napr., 66, VINITI, M., 1991, 148–187 | MR | Zbl
[21] Grines V. Z., “O topologicheskoi sopryazhennosti diffeomorfizmov dvumernogo mnogoobraziya na odnomernykh bazisnykh mnozhestvakh”, UMN, 29:6 (1974), 163–164 | MR | Zbl
[22] Mañé R., “A proof of $C^1$ stability conjecture”, Publ. Math. Inst. Hautes Étud. Sci., 66 (1988), 161–210 | DOI | MR | Zbl
[23] Robinson C., “Structural stability of $C^1$ diffeomorphisms”, J. Differential Equations, 22:1 (1976), 28–73 | DOI | MR | Zbl
[24] Keldysh L. V., Topologicheskie vlozheniya v evklidovo prostranstvo, Tr. MIAN, 81, Nauka, M., 1966 | Zbl
[25] Grines V. Z., Zhuzhoma E. V., “O topologicheskoi klassifikatsii orientiruemykh attraktorov na $n$-mernom tore”, UMN, 34:4 (1979), 185–186 | MR
[26] Rosenberg H., “Foliations by planes”, Topology, 7 (1968), 131–138 | DOI | MR | Zbl
[27] Tamura I., Topologiya sloenii, Mir, M., 1979 | MR | Zbl
[28] Aranson S., Belitsky G., Zhuzhoma E., Introduction to the qualitative theory of dynamical systems on surfaces, Transl. Math. Monogr., 153, Amer. Math. Soc., Providence, RI, 1996 | MR | Zbl
[29] Novikov S. P., “Topologiya sloenii”, Tr. MMO, 14, URSS, M., 1965, 248–278 | MR | Zbl
[30] Aranson S. Kh., Zhuzhoma E. V., “O topologicheskoi klassifikatsii sloenii Riba korazmernosti odin na trekhmernom tore”, Metody kachestvennoi teorii differentsialnykh uravnenii, Mezhvuz. matem. sb., ed. E. A. Leontovich-Andronova, Gorkii, 1978, 41–64 | Zbl
[31] Grines V., Zhuzhoma E., Structuraly stable diffeomorphisms with codimension one basic sets, Preprint No223, Université de Bourgogne, Laboratoire de topologie, Dijon Cedex, 2000
[32] Hirsch M., Pugh C., “Stable manifolds and hyperbolic sets”, Global analysis, Proc. Sympos. Pure Math., 14, 1970, 133–163 | MR | Zbl
[33] Hempel J., 3-manifolds, Ann. of Math. Stud., 86, Princeton Univ. Press; Univ. Tokyo Press, Princeton, NJ, 1976 | MR | Zbl
[34] Franks J., Robinson C., “A quasi-Anosov diffeomorphism that is not Anosov”, Trans. Amer. Math. Soc., 223 (1976), 267–278 | DOI | MR | Zbl
[35] de Melo W., “Structural stability of diffeomorphisms on two-manifolds”, Invent. Math., 21 (1973), 233–246 | DOI | MR | Zbl
[36] Spener E., Algebraicheskaya topologiya, Mir, M., 1971 | MR | Zbl
[37] Grines V. Z., “O topologicheskoi klassifikatsii strukturno ustoichivykh diffeomorfizmov poverkhnostei s odnomernymi attraktorami i repellerami”, Matem. sb., 188 (1997), 57–94 | MR | Zbl
[38] Hirch M., Palis J., Pugh C., Shub M., “Neighborhoods of hyperbolic sets”, Invent. Math., 9 (1970), 121–134 | DOI | MR
[39] Williams R. F., “The $DA$-maps of Smale and structural stability”, Proc. Berk. Symp., 14 (1970), 329–334 | MR | Zbl
[40] Zhuzhoma E. V., “Orientiruemye bazisnye mnozhestva korazmernosti 1”, Izvestiya VUZov, Matematika, 1982, no. 5, 16–21 | MR | Zbl
[41] Zhirov A. Yu., “Complete combinatorial invariants for conjugacy of hyperbolic attractors of diffeomorphisms of surfaces”, Journ. Dyn. and Contr. Syst., 6:3 (2000), 397–430 \endcomment | DOI | MR | Zbl