@article{SM_2016_207_5_a3,
author = {E. V. Zhuzhoma and V. S. Medvedev},
title = {Continuous {Morse-Smale} flows with three equilibrium positions},
journal = {Sbornik. Mathematics},
pages = {702--723},
year = {2016},
volume = {207},
number = {5},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2016_207_5_a3/}
}
E. V. Zhuzhoma; V. S. Medvedev. Continuous Morse-Smale flows with three equilibrium positions. Sbornik. Mathematics, Tome 207 (2016) no. 5, pp. 702-723. http://geodesic.mathdoc.fr/item/SM_2016_207_5_a3/
[1] D. V. Anosov, “Iskhodnye ponyatiya. Elementarnaya teoriya”, Gl. 1, 2, Dinamicheskie sistemy – 1, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 1, VINITI, M., 1985, 156–204 | MR | Zbl
[2] V. V. Nemytskii, V. V. Stepanov, Qualitative theory of differential equations, Princeton Mathematical Series, 22, Princeton Univ. Press, Princeton, NJ, 1960, viii+523 pp. | MR | MR | Zbl | Zbl
[3] J. Milnor, “On manifolds homeomorphic to the 7-sphere”, Ann. of Math. (2), 64:2 (1956), 399–405 | DOI | MR | Zbl
[4] D. V. Anosov, “Structurally stable systems”, Proc. Steklov Inst. Math., 169 (1986), 61–95 | MR | Zbl
[5] C. Robinson, Dynamical systems. Stability, symbolic dynamics, and chaos, Stud. Adv. Math., 2nd ed., CRC Press, Boca Raton, FL, 1999, xiv+506 pp. | MR | Zbl
[6] M. W. Hirsch, C. C. Pugh, M. Shub, Invariant manifolds, Lecture Notes in Math., 583, Springer-Verlag, Berlin–New York, 1977, ii+149 pp. | MR | Zbl
[7] S. Smale, “Differentiable dynamical systems”, Bull. Amer. Math. Soc., 73:6 (1967), 747–817 | DOI | MR | MR | Zbl
[8] S. Smale, “Morse inequalities for a dynamical system”, Bull. Amer. Math. Soc., 66 (1960), 43–49 | DOI | MR | Zbl
[9] E. V. Zhuzhoma, V. S. Medvedev, “Global dynamics of Morse–Smale systems”, Proc. Steklov Inst. Math., 261 (2008), 112–135 | DOI | MR | Zbl
[10] J. Eells, Jr., N. H. Kuiper, “Manifolds which are like projective planes”, Inst. Hautes Études Sci. Publ. Math., 14 (1962), 5–46 | DOI | MR | Zbl
[11] D. Pixton, “Wild unstable manifolds”, Topology, 16:2 (1977), 167–172 | DOI | MR | Zbl
[12] V. Z. Grines, O. V. Pochinka, Vvedenie v topologicheskuyu klassifikatsiyu diffeomorfizmov na mnogoobraziyakh razmernosti dva i tri, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2011, 424 pp.
[13] E. V. Zhuzhoma, V. S. Medvedev, “Gradient flows with wildly embedded closures of separatrices”, Proc. Steklov Inst. Math., 270 (2010), 132–140 | DOI | MR | Zbl
[14] E. V. Zhuzhoma, V. S. Medvedev, “Morse–Smale systems with three nonwandering points”, Dokl. Math., 84:2 (2011), 604–606 | DOI | Zbl
[15] M. W. Hirsch, Differential topology, Grad. Texts in Math., 33, Springer-Verlag, New York–Heidelberg, 1976, x+221 pp. | DOI | MR | MR | Zbl | Zbl
[16] M. H. Freedman, “The topology of four-dimensional manifolds”, J. Differential Geom., 17:3 (1982), 357–453 | MR | Zbl
[17] M. H. A. Newman, “The engulfing theorem for topological manifolds”, Ann. of Math. (2), 84:3 (1966), 555–571 | DOI | MR | Zbl
[18] G. Perelman, Ricci flow with surgery on three-manifolds, 2003, arXiv: math.DG/0303109
[19] G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, 2003, arXiv: math.DG/0307245
[20] S. Smale, “Generalized Poincaré's conjecture in dimensions greater than four”, Ann. of Math. (2), 74:2 (1961), 391–406 | DOI | MR | Zbl
[21] J. F. Adams, “On the non-existence of elements of Hopf invariant one”, Ann. of Math. (2), 72:1 (1960), 20–104 | DOI | MR | Zbl
[22] S. P. Novikov, Topologiya, 2-e izd., In-t kompyuternykh issledovanii, M.–Izhevsk, 2002, 336 pp.
[23] C. Bonatti, V. Z. Grines, V. S. Medvedev, E. Pecou, “On the topological classification of gradient-like diffeomorphisms without heteroclinic curves on three-dimensional manifolds”, Dokl. Math., 63:2 (2001), 161–164 | MR | Zbl
[24] Ch. Bonatti, V. Z. Grines, V. S. Medvedev, E. Peku, “On Morse–Smale diffeomorphisms without heteroclinic intersections on three-manifolds”, Proc. Steklov Inst. Math., 236 (2002), 58–69 | MR | Zbl
[25] V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “On Morse–Smale diffeomorphisms with four periodic points on closed orientable manifolds”, Math. Notes, 74:3 (2003), 352–366 | DOI | DOI | MR | Zbl
[26] L. V. Keldysh, “Topological imbeddings in Euclidean space”, Proc. Steklov Inst. Math., 81 (1966), 1–203 | MR | Zbl
[27] R. J. Daverman, G. A. Venema, Embeddings in manifolds, Grad. Stud. Math., 106, Amer. Math. Soc., Providence, RI, 2009, xviii+468 pp. | DOI | MR | Zbl
[28] Ch. Bonatti, V. Grines, V. Medvedev, E. Pécou, “Three-manifolds admitting Morse–Smale diffeomorphisms without heteroclinic curves”, Topology Appl., 117:3 (2002), 335–344 | DOI | MR | Zbl
[29] A. V. Chernavskii, “Singular points of topological imbeddings of manifolds and the union of locally flat cells”, Soviet Math. Dokl., 7 (1966), 433–436 | MR | Zbl
[30] J. C. Cantrell, “Almost locally flat embeddings of $S^{n-1}$ in $S^n$”, Bull. Amer. Math. Soc., 69:5 (1963), 716–718 | DOI | MR | Zbl
[31] J. Cantrell, C. Edwards, “Almost locally flat imbeddings of manifolds”, Michigan Math. J., 12 (1965), 217–223 | DOI | MR | Zbl
[32] 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
[33] J. Palis, Jr., W. de Melo, Geometric theory of dynamical systems. An introduction, Springer-Verlag, New York–Berlin, 1982, xii+198 pp. | MR | MR | Zbl
[34] C. McA. Gordon, J. Luecke, “Knots are determinned by their complements”, J. Amer. Math. Soc., 2:2 (1989), 371–415 | DOI | MR | Zbl
[35] P. B. Kronheimer, T. S. Mrowka, “Witten's conjecture and property P”, Geom. Topol., 8 (2004), 295–310 | DOI | MR | Zbl
[36] S. Kh. Aranson, G. R. Belitsky, E. V. Zhuzhoma, Introduction to qualitative theory of dynamical systems on closed surfaces, Transl. Math. Monogr., 153, Amer. Math. Soc., Providence, RI, 1996, xiv+325 pp. | MR | Zbl