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@article{TRSPY_2010_270_a8, author = {E. V. Zhuzhoma and V. S. Medvedev}, title = {Gradient flows with wildly embedded closures of separatrices}, journal = {Informatics and Automation}, pages = {138--146}, publisher = {mathdoc}, volume = {270}, year = {2010}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a8/} }
E. V. Zhuzhoma; V. S. Medvedev. Gradient flows with wildly embedded closures of separatrices. Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 138-146. http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a8/
[1] Anosov D.V., “Iskhodnye ponyatiya. Elementarnaya teoriya”, Dinamicheskie sistemy – 1, Itogi nauki i tekhniki. Sovr. probl. matematiki. Fund. napr., 1, VINITI, M., 1985, 156–178; 178–204
[2] Anosov D.V., Solodov V.V., “Giperbolicheskie mnozhestva”, Dinamicheskie sistemy – 9, Itogi nauki i tekhniki. Sovr. probl. matematiki. Fund. napr., 66, VINITI, M., 1991, 12–99 | MR
[3] Bonatti Kh., Grines V.Z., Medvedev V.C., Peku E., “O topologicheskoi klassifikatsii gradientnopodobnykh diffeomorfizmov bez geteroklinicheskikh krivykh na trekhmernykh mnogoobraziyakh”, DAN, 377:2 (2001), 151–155 | MR | Zbl
[4] Bonatti Kh., Grines V.Z., Medvedev V.C., Peku E., “O diffeomorfizmakh Morsa–Smeila bez geteroklinicheskikh peresechenii na trekhmernykh mnogoobraziyakh”, Tr. MIAN, 236, 2002, 66–78 | MR | Zbl
[5] Bonatti Kh., Grines V.Z., Pochinka O.V., “Klassifikatsiya diffeomorfizmov Morsa–Smeila s konechnym mnozhestvom geteroklinicheskikh orbit na 3-mnogoobraziyakh”, Tr. MIAN, 250, 2005, 5–53 | MR | Zbl
[6] Grines V.Z., Zhuzhoma E.V., Medvedev V.C., “O diffeomorfizmakh Morsa–Smeila s chetyrmya periodicheskimi tochkami na zamknutykh orientiruemykh mnogoobraziyakh”, Mat. zametki, 74:3 (2003), 369–386 | DOI | MR | Zbl
[7] Palis Zh., di Melu V., Geometricheskaya teoriya dinamicheskikh sistem: Vvedenie, Mir, M., 1986 | MR
[8] Pontryagin L.S., Gladkie mnogoobraziya i ikh primeneniya v teorii gomotopii, Tr. MIAN, 45, Izd-vo AN SSSR, M., 1955 | MR
[9] Chernavskii A.V., “Ob osobykh tochkakh topologicheskikh vlozhenii mnogoobrazii i ob'edinenii lokalno ploskikh kletok”, DAN SSSR, 167:3 (1966), 528–530
[10] Andrews J.J., Curtis M.L., “Knotted 2-spheres in the 4-sphere”, Ann. Math. Ser. 2, 70:3 (1959), 565–571 | DOI | MR | Zbl
[11] Artin E., “Zur Isotopie zweidimensionaler Flächen im $R_4$”, Abh. Math. Sem. Univ. Hamburg, 4 (1925), 174–177 | DOI | Zbl
[12] Bonatti C., Grines V., “Knots as topological invariant for gradient-like diffeomorphisms of the sphere $S^3$”, J. Dyn. and Control Syst., 6 (2000), 579–602 | DOI | MR | Zbl
[13] Bonatti C., Grines V., Medvedev V., Pécou E., “Three-manifolds admitting Morse–Smale diffeomorphisms without heteroclinic curves”, Topol. and Appl., 117 (2002), 335–344 | DOI | MR | Zbl
[14] Bonatti C., Grines V., Medvedev V., Pécou E., “Topological classification of gradient-like diffeomorphisms on 3-manifolds”, Topology, 43 (2004), 369–391 | DOI | MR | Zbl
[15] Eells J., Jr., Kuiper N.H., “Manifolds which are like projective planes”, Publ. Math. IHES., 14 (1962), 5–46 | DOI | MR
[16] Gordon C.McA., Luecke J., “Knots are determinned by their complements”, J. Amer. Math. Soc., 2 (1989), 371–415 | DOI | MR | Zbl
[17] Hirsch M.W., Differential topology, Grad. Texts Math., 33, Springer, New York, 1976 ; Khirsh M., Differentsialnaya topologiya, Mir, M., 1979 | DOI | MR | Zbl | MR
[18] Kronheimer P.B., Mrowka T.S., “Witten's conjecture and property P”, Geom. and Topol., 8 (2004), 295–310 | DOI | MR | Zbl
[19] Pixton D., “Wild unstable manifolds”, Topology, 16 (1977), 167–172 | DOI | MR | Zbl
[20] Reeb G., “Sur certaines propriétés topologiques des variétés feuilletées”: Wu W.-T., Reeb G., Sur les espaces fibrés et les variétés feuilletées, Actual. sci. et ind., 1183, Hermann, Paris, 1952, 91–154 | MR
[21] Robinson C., Dynamical systems: Stability, symbolic dynamics, and chaos, Stud. Adv. Math., 2nd ed., CRC Press, Boca Raton (FL), 1999 | MR | Zbl
[22] Smale S., “On gradient dynamical systems”, Ann. Math. Ser. 2, 74 (1961), 199–206 | DOI | MR | Zbl
[23] Smale S., “Differentiable dynamical systems”, Bull. Amer. Math. Soc., 73:6 (1967), 747–817 ; Smeil S., “Differentsiruemye dinamicheskie sistemy”, UMN, 25:1 (1970), 113–185 | DOI | MR | Zbl | MR
[24] Stallings J., “On topologically unknotted spheres”, Ann. Math. Ser. 2, 77 (1963), 490–503 | DOI | MR | Zbl