Email this article Knot as a complete invariant of a Morse-Smale 3-diffeomorphism with four fixed points
- Authors: Pochinka O.V.1, Talanova E.A.1,2, Shubin D.D.1
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Affiliations:
- National Research University – Higher School of Economics in Nizhny Novgorod
- National Research Lobachevsky State University of Nizhny Novgorod
- Issue: Vol 214, No 8 (2023)
- Pages: 94-107
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133545
- DOI: https://doi.org/10.4213/sm9814
- ID: 133545
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Abstract
It is known that the topological conjugacy class of a Morse-Smale flows with unique saddle is defined by the equivalence class of the Hopf knot in
About the authors
Olga Vital'evna Pochinka
National Research University – Higher School of Economics in Nizhny Novgorod
Author for correspondence.
Email: olga-pochinka@yandex.ru
Doctor of physico-mathematical sciences, no status
Elena Anatol'evna Talanova
National Research University – Higher School of Economics in Nizhny Novgorod; National Research Lobachevsky State University of Nizhny Novgorod
Email: eltalanova72@gmail.com
Danila Denisovich Shubin
National Research University – Higher School of Economics in Nizhny Novgorod
Email: schub.danil@yandex.ru
References
- C. Bonatti, V. Grines, O. Pochinka, “Topological classification of Morse–Smale diffeomorphisms on 3-manifolds”, Duke Math. J., 168:13 (2019), 2507–2558
- P. Kirk, C. Livingston, “Knot invariants in 3-manifolds and essential tori”, Pacific J. Math., 197:1 (2001), 73–96
- P. M. Akhmet'ev, T. V. Medvedev, O. V. Pochinka, “On the number of the classes of topological conjugacy of Pixton diffeomorphisms”, Qual. Theory Dyn. Syst., 20:3 (2021), 76, 15 pp.
- B. Mazur, “A note on some contractible 4-manifolds”, Ann. of Math. (2), 73:1 (1961), 221–228
- C. Bonatti, V. Z. Grines, “Knots as topological invariants for gradient-like diffeomorphisms of the sphere $S^3$”, J. Dynam. Control Systems, 6:4 (2000), 579–602
- D. Pixton, “Wild unstable manifolds”, Topology, 16:2 (1977), 167–172
- В. З. Гринес, Е. В. Жужома, В. C. Медведев, “О диффеоморфизмах Морса–Смейла с четырьмя периодическими точками на замкнутых ориентируемых многообразиях”, Матем. заметки, 74:3 (2003), 369–386
- V. S. Afraimovich, M. I. Rabinovich, P. Varona, “Heteroclinic contours in neural ensembles and the winnerless competition principle”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 14:4 (2004), 1195–1208
- V. Z. Grines, T. V. Medvedev, O. V. Pochinka, Dynamical systems on 2- and 3-manifolds, Dev. Math., 46, Springer, Cham, 2016, xxvi+295 pp.
- B. Шмуклер, O. Починка, “Бифуркации, меняющие тип гетероклинических кривых 3-диффеоморфизмов Морса–Смейла”, Таврический вестник информатики и математики, 50:1 (2021), 101–114
- T. V. Medvedev, O. V. Pochinka, “The wild Fox–Artin arc in invariant sets of dynamical systems”, Dyn. Syst., 33:4 (2018), 660-666
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