Abstract:
Continuous Morse-Smale flows on closed manifolds whose nonwandering set consists of three equilibrium positions are considered. Necessary and sufficient conditions for topological equivalence of such flows are obtained and the topological structure of the underlying manifolds is described.
Bibliography: 36 titles.
This research was supported by the Russian Foundation for Basic Research (grant no. 15-01-03687-a) and the Russian Science Foundation (project no. 14-41-00044) within the framework of the Programme of Federal Research of the National Research University “Higher School of Economics” in 2016 (T3-98).
This publication is cited in the following 18 articles:
E. Ya. Gurevich, I. A. Saraev, “Kirby diagram of polar flows on four-dimensional manifolds”, Math. Notes, 116:1 (2024), 40–57
V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “On Diffeomorphisms with Orientable Codimension 1 Basic Sets and an Isolated Saddle”, Proc. Steklov Inst. Math., 327 (2024), 55–69
Vladislav S. Medvedev, Evgeny V. Zhuzhoma, “Smale Regular and Chaotic A-Homeomorphisms and A-Diffeomorphisms”, Regul. Chaotic Dyn., 28:2 (2023), 131–147
E. V. Zhuzhoma, V. S. Medvedev, “Many-Dimensional Morse–Smale Diffeomeophisms with a Dominant Saddle”, Math. Notes, 111:6 (2022), 870–878
V. Z. Grines, E. Ya. Gurevich, “Topological classification of flows without heteroclinic intersections on a connected sum of manifolds Sn−1×S1”, Russian Math. Surveys, 77:4 (2022), 759–761
V. Z. Grines, E. Ya. Gurevich, “On classification of Morse–Smale flows on projective-like manifolds”, Izv. Math., 86:5 (2022), 876–902
Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma, “On the Topological Structure of Manifolds Supporting Axiom A Systems”, Regul. Chaotic Dyn., 27:6 (2022), 613–628
V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “On Embedding of the Morse–Smale Diffeomorphisms in a Topological Flow”, J Math Sci, 265:6 (2022), 868
V. Medvedev, E. Zhuzhoma, “High-dimensional Morse-Smale systems with king-saddles”, Topology and its Applications, 312 (2022), 108080
E. V. Zhuzhoma, V. S. Medvedev, “Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms”, Sb. Math., 212:1 (2021), 57–69
V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “On Realization of Topological Conjugacy Classes of Morse–Smale Cascades on the Sphere Sn”, Proc. Steklov Inst. Math., 310 (2020), 108–123
V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “O vklyuchenii diffeomorfizmov Morsa—Smeila v topologicheskii potok”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 66, no. 2, Rossiiskii universitet druzhby narodov, M., 2020, 160–181
V. Medvedev, E. Zhuzhoma, “Supporting manifolds for high-dimensional morse-smale diffeomorphisms with few saddles”, Topology Appl., 282 (2020), 107315
V. Z. Grines, E. Ya. Gurevich, E. V. Zhuzhoma, O. V. Pochinka, “Classification of Morse–Smale systems and topological structure of the underlying manifolds”, Russian Math. Surveys, 74:1 (2019), 37–110
V. Grines, E. Gurevich, O. Pochinka, “On embedding of multidimensional Morse–Smale diffeomorphisms into topological flows”, Mosc. Math. J., 19:4 (2019), 739–760
E. V. Zhuzhoma, V. S. Medvedev, “Conjugacy of Morse–Smale Diffeomorphisms with Three Nonwandering Points”, Math. Notes, 104:5 (2018), 753–757
V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “An Analog of Smale's Theorem for Homeomorphisms with Regular Dynamics”, Math. Notes, 102:4 (2017), 569–574
V. Z. Grines, E. V. Zhuzhoma, O. V. Pochinka, “Sistemy Morsa–Smeila i topologicheskaya struktura nesuschikh mnogoobrazii”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 61, RUDN, M., 2016, 5–40
Citation in format AMSBIB
Contact us: