Geodesic
Morse--Smale Diffeomorphisms with Three Fixed Points
Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 541-558.

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It is proved that the closures of separatrices for a Morse–Smale diffeomorphism with three fixed points are flatly embedded spheres if the dimension of the manifold is at least 6 and may be wildly embedded spheres if the dimension of the manifold is 4.
Keywords: Morse–Smale diffeomorphism with three fixed points, separatrix of a saddle, flatly embedded sphere, wildly embedded sphere, nonwandering set, periodic point. 
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E. V. Zhuzhoma; V. S. Medvedev. Morse--Smale Diffeomorphisms with Three Fixed Points. Matematičeskie zametki, Tome 92 (2012) no. 4, pp. 541-558. http://geodesic.mathdoc.fr/item/MZM_2012_92_4_a5/

[1] D. V. Anosov, “Gladkie dinamicheskie sistemy. Gl. 1. Iskhodnye ponyatiya”, Dinamicheskie sistemy – 1, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 1, VINITI, M., 1985, 156–178

[2] D. V. Anosov, V. V. Solodov, “Dinamicheskie sistemy s giperbolicheskim povedeniem. Gl. 1. Giperbolicheskie mnozhestva”, Dinamicheskie sistemy – 9, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 66, VINITI, M., 1991, 12–99 | MR | Zbl

[3] S. Smale, “Differentiable dynamical systems”, Bull. Amer. Math. Soc., 73 (1967), 741–817 ; S. Smeil, “Differentsiruemye dinamicheskie sistemy”, UMN, 25:1 (1970), 113–185 | MR | Zbl | MR

[4] V. Z. Grines, E. V. Zhuzhoma, V. C. Medvedev, “O diffeomorfizmakh Morsa–Smeila s chetyrmya periodicheskimi tochkami na zamknutykh orientiruemykh mnogoobraziyakh”, Matem. zametki, 74:3 (2003), 369–386 | MR | Zbl

[5] D. Pixton, “Wild unstable manifolds”, Topology, 16:2 (1977), 167–172 | DOI | MR | Zbl

[6] Kh. Bonatti, V. Z. Grines, V. C. Medvedev, E. Peku, “O topologicheskoi klassifikatsii gradientnopodobnykh diffeomorfizmov bez geteroklinicheskikh krivykh na trekhmernykh mnogoobraziyakh”, DAN, 377:2 (2001), 151–155 | MR | Zbl

[7] Kh. Bonatti, V. Z. Grines, V. C. Medvedev, E. Peku, “O diffeomorfizmakh Morsa–Smeila bez geteroklinicheskikh peresechenii na trekhmernykh mnogoobraziyakh”, Differentsialnye uravneniya i dinamicheskie sistemy, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Evgeniya Frolovicha Mischenko, Tr. MIAN, 236, Nauka, M., 2002, 66–78 | MR | Zbl

[8] Kh. Bonatti, V. Z. Grines, O. V. Pochinka, “Klassifikatsiya diffeomorfizmov Morsa–Smeila s konechnym mnozhestvom geteroklinicheskikh orbit na 3-mnogoobraziyakh”, Differentsialnye uravneniya i dinamicheskie sistemy, Sbornik statei, Tr. MIAN, 250, Nauka, M., 2005, 5–53 | MR | Zbl

[9] C. Bonatti, V. Grines, “Knots as topological invariant for gradient-like diffeomorphisms of the sphere $S^3$”, J. Dynam. Control Systems, 6:4 (2000), 579–602 | DOI | MR | Zbl

[10] C. Bonatti, V. Grines, V. Medvedev, E. Pécou, “Topological classification of gradient-like diffeomorphisms on 3-manifolds”, Topology, 43:2 (2004), 369–391 | DOI | MR | Zbl

[11] C. Bonatti, V. Grines, V. Medvedev, E. Pécou, “Three-dimensional manifolds admitting Morse–Smale diffeomorphisms without heteroclinic curves”, Topology Appl., 117:3 (2002), 335–344 | DOI | MR | Zbl

[12] J. Eells, N. H. Kuiper, “Manifolds which are like projective planes”, Inst. Hautes Études Sci. Publ. Math., 14 (1962), 5–46 | MR | Zbl

[13] V. Z. Grines, E. V. Zhuzhoma, V. C. Medvedev, O. V. Pochinka, “Globalnye attraktor i repeller diffeomorfizmov Morsa–Smeila”, Differentsialnye uravneniya i topologiya. II, Sbornik statei. K 100-letiyu so dnya rozhdeniya akademika Lva Semenovicha Pontryagina, Tr. MIAN, 271, M., 2010, 111–133 | MR

[14] R. Abraham, S. Smale, “Nongeneracity of $\Omega$-stability”, Global Analysis, Proc. Sympos. Pure Math., 14, Amer. Math. Soc., Providence, RI, 1970, 5–8 | MR | Zbl

[15] S. Smale, “Morse inequalities for a dynamical system”, Bull. Amer. Math. Soc., 66 (1960), 43–49 | DOI | MR | Zbl

[16] J. C. Cantrell, “Almost locally flat embeddings of $S^{n-1}$ in $S^n$”, Bull. Amer. Math. Soc., 69 (1963), 716–718 | DOI | MR | Zbl

[17] R. J. Daverman, G. A. Venema, Embeddings in Manifolds, Grad. Stud. Math., 106, Amer. Math. Soc., Providence, RI, 2009 | MR | Zbl

[18] A. T. Fomenko, D. B. Fuks, Kurs gomotopicheskoi topologii, Nauka, M., 1989 | MR | Zbl

[19] L. V. Keldysh, Topologicheskie vlozheniya v evklidovo prostranstvo, Tr. MIAN SSSR, 81, 1966 | MR | Zbl

[20] A. V. Chernavskii, “Ob osobykh tochkakh topologicheskikh vlozhenii mnogoobrazii i ob'edinenii lokalno ploskikh kletok”, DAN SSSR, 167:3 (1966), 528–530 | MR | Zbl

[21] J. Stallings, “On topologically unknotted spheres”, Ann. of Math. (2), 77:3 (1963), 490–503 | DOI | MR | Zbl

[22] J. C. Cantrell, C. H. Edwards, Jr., “Almost locally flat imbeddings of manifolds”, Michigan Math. J., 12:2 (1965), 217–223 | DOI | MR | Zbl

[23] R. H. Fox, E. Artin, “Some wild cells and spheres in three-dimensional space”, Ann. of Math. (2), 49:4 (1948), 979–990 | DOI | MR | Zbl

[24] J. J. Andrews, M. L. Curtis, “Knotted 2-spheres in the 4-sphere”, Ann. of Math. (2), 70:3 (1959), 565–571 | DOI | MR | Zbl

[25] M. Hirsch, “Differential Topology”, Grad. Texts in Math., 33, Springer-Verlag, New York, 1976 ; M. Khirsh, Differentsialnaya topologiya, Mir, M., 1979 | MR | Zbl | MR | Zbl

[26] V. A. Rokhlin, D. B. Fuks, Nachalnyi kurs topologii. Geometricheskie glavy, Nauka, M., 1977 | MR | Zbl