Geodesic
On Morse–Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 369-386 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study Morse–Smale diffeomorphisms of n-manifolds with four periodic points which are the only periodic points. We prove that for $n= 3$ these diffeomorphisms are gradient-like and define a class of diffeomorphisms inevitably possessing a nonclosed heteroclinic curve. For $n\ge4$, we construct a complete conjugacy invariant in the class of diffeomorphisms with a single saddle of codimension one. 
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     title = {On {Morse{\textendash}Smale} {Diffeomorphisms} with {Four} {Periodic} {Points} on {Closed} {Orientable} {Manifolds}},
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V. Z. Grines; E. V. Zhuzhoma; V. S. Medvedev. On Morse–Smale Diffeomorphisms with Four Periodic Points on Closed Orientable Manifolds. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 369-386. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a5/

[1] Smale S., “Differentiable dynamical systems”, Bull. Amer. Math. Soc., 73:1 (1967), 741–817 | MR

[2] Bezdenezhnykh A. N., Grines V. Z., “Dinamicheskie svoistva i topologicheskaya klassifikatsiya gradientnopodobnykh diffeomorfizmov na dvumernykh mnogoobraziyakh. I; II”, Metody KTDU, ed. E. A. Lentovich-Andronova, GGU, Gorkii, 1985, 22–38; 1987, 24–32 | MR

[3] Bezdenezhnykh A. N., Grines V. Z., “Realizatsiya gradientnopodobnykh diffeomorfizmov dvumernykh mnogoobrazii”, Differents. i integralnye uravneniya, ed. N. F. Otrokov, GGU, Gorkii, 1985, 33–37 | MR

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

[5] Bonatti Ch., Grines V. Z., “Knots as topological invariant for gradient-like diffeomorphisms of the sphere $S^3$”, J. of Dyn. and Control Syst., 6 (2000), 579–602 | DOI | MR | Zbl

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

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

[8] Nitetski Z., Vvedenie v differentsialnuyu dinamiku, Mir, M., 1975 | Zbl

[9] Anosov D. V., “Iskhodnye ponyatiya. Elementarnaya teoriya”, Dinamicheskie sistemy–1, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 1, 1985, 156–178 ; 178–204

[10] Aranson S. Kh., Grines V. Z., “Kaskady na poverkhnostyakh”, Dinamicheskie sistemy–9, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 66, 1991, 148–187

[11] Keldysh L. V., Topologicheskie vlozheniya v evklidovo prostranstvo, Tr. MIAN, 81, Nauka, M., 1966 | MR

[12] Bonatti Ch., Grines V. Z., Medvedev V., Pecou E., “Three-dimensional manifolds admitting Morse–Smale diffeomorphisms without heteroclinic curves”, Topology and applications, 117 (2002), 335–344 | DOI | MR

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

[14] Cantrell J. C., Edwards C. H., “Almost locally polyhedral curves in Euclidean $n$-space”, Trans. Amer. Math. Soc., 107:3 (1963), 451–457 | DOI | MR | Zbl

[15] Gugenheim V., “Piecewise linear isotopy and embedding of elements and spheres, I”, Proc. London Math. Soc., 3 (1953), 29–53 | DOI | MR | Zbl