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JOURNALS // Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva

Zhurnal SVMO, 2011, Volume 13, Number 2, Pages 17–24 (Mi svmo233)

Complete topological invariant for Morse-Smale diffeomorphisms on 3-manifolds
O. V. Pochinka

References

1. Andronov A. A., Pontryagin L. S., “Grubye sistemy”, Dokl. AN SSSR, 14:5 (1937), 247–250
2. Bezdenezhnykh A. N., Grines V. Z., “Dinamicheskie svoistva i topologicheskaya klassifikatsiya gradientnopodobnykh diffeomorfizmov na dvumernykh mnogoobraziyakh. Chast 1”, Metody kachestvennoi teorii differents. uravnenii. Mezhvuz. temat. sb. nauchn. tr. pod red. E.A. Lentovich-Andronovoi, 1985, 22–38, Gorkii
3. Bezdenezhnykh A. N., Grines V. Z., “Realizatsiya gradientnopodobnykh diffeomorfizmov dvumernykh mnogoobrazii”, Differentsialnye i integralnye uravneniya. Sb. nauch. tr. pod red. N.F. Otrokova, 1985, 33–37, Gorkii GGU
4. Bezdenezhnykh A. N., Grines V. Z., “Dinamicheskie svoistva i topologicheskaya klassifikatsiya gradientnopodobnykh diffeomorfizmov na dvumernykh mnogoobraziyakh. Chast 2”, Metody kachestvennoi teorii differents. uravnenii. Mezhvuz. temat. sb. nauchn. tr. pod red. E.A. Lentovich-Andronovoi, 1987, 24–32, Gorkii
5. Bonatti Ch., Grines V., “Knots as topological invariant for gradient-like diffeomorphisms of the sphere S^3”, Journal of Dynamical and Control Systems (Plenum Press, New York and London), 6:4 (2000), 579–602
6. Bonatti Ch., Grines V., Medvedev V., Pecou E., “Topological classification of gradient-like diffeomorphisms on 3–manifolds”, Topology, 2004, no. 43, 369–391
7. Bonatti Khr., Grines V. Z., Pochinka O.\V., “lassifikatsiya diffeomorfizmov Morsa-Smeila s konechnym mnozhestvom geteroklinicheskikh orbit na 3-mnogoobraziyakh”, Trudy MIAN, 2005, no. 250, 5–53  mathnet
8. Bonatti Ch., Grines V., Pochinka O., “Classification of Morse-Smale diffeomorphisms with the chain of saddles on 3-manifolds”, Foliations 2005. World Scientific, Singapore, 2006, 121–147
9. Bonatti Ch., Paoluzzi L., “3-manifolds which are orbit spaces of diffeomorphisms”, Topology, 47 (2008), 71–100
10. Grines V.\Z., “Topologicheskaya klassifikatsiya diffeomopfizmov Mopsa-Smeila s konechnym mnozhestvom getepoklinicheskikh tpaektopii na povepkhnostyakh”, Matem. zametki., 54:3 (1993), 3–17  mathnet
11. Grines V.\Z., Gurevich E.\Ya., “O diffeomorfizmakh Morsa-Smeila na mnogoobraziyakh razmernosti bolshei trekh”, Doklady akademii nauk, 416:1 (2007), 15–17  mathnet
12. Grines V.\Z., Gurevich E.\Ya., Medvedev V.§., “Graf Peikshoto diffeomorfizmov Morsa-Smeila na mnogoobraziyakh razmernosti bolshei trekh”, Trudy matematicheskogo instituta im. V.A.Steklova, 261 (2008), 61–86  mathnet
13. Leontovich E.\A., Maier A.\G., “O skheme, oppedelyayuschei topologicheskuyu stpuktupu pazbieniya na tpaektopii”, Dokl. AN SSSP, 103:4 (1955), 557–560
14. Maier A.\G., “Gpuboe ppeobpazovanie okpuzhnosti v okpuzhnost”, Uch. Zap. GGU, 1939, no. 12, 215–229, Izd-vo GGU, Gopkii
15. Peixoto M., “On the classification of flows on two-manifolds”, Dynamical systems Proc. Symp. held at the Univ.of Bahia, Salvador, Brasil, 1973, 389–419, Acad. press, N.Y.London
16. Pilyugin S.\Yu., “Fazovye diagrammy, opredelyayuschie sistemy Morsa-Smeila bez periodicheskikh traektorii na sferakh”, Differentsialnye uravneniya, 14:2 (1978), 245–254  mathnet
17. Pixton D., “Wild unstable manifolds”, Topology, 16:2 (1977), 167–172
18. Smeil S., “Neravenstva Morsa dlya dinamicheskikh sistem”, Sb. Matematika, 11:4 (1967), 79–87
19. Umanskii Ya.Ł., “Neobkhodimye i dostatochnye usloviya topologicheskoi ekvivalentnosti trekhmernykh dinamicheskikh sistem Morsa-Smeila s konechnym chislom osobykh traektorii”, Mat. sb., 181:2 (1990), 212–239  mathnet


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