Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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Topology of Morse-Smale flows with singularities on the boundary of the two-dimensional disk

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PDF (Українська)
Published Jan 20, 2017
DOI https://doi.org/10.15673/tmgc.v9i2.279

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Mariia Losieva
Taras Shevchenko National University of Kyiv
http://orcid.org/0000-0002-2282-206X
Oleksandr Prishlyak
Taras Shevchenko National University of Kyiv
http://orcid.org/0000-0002-7164-807X

Abstract

We analyze the topological properties of Morse-Smale flows on two-dimensional disk, which singularities lying on the boundary of the disc. We construct a complete topological invariant of the flow. The topological classification of the flows is obtained. The method of numbering flows is proposed.
Keywords:
Topological classification, flow, surface with boundary

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How to Cite
Losieva, M., & Prishlyak, O. (2017). Topology of Morse-Smale flows with singularities on the boundary of the two-dimensional disk. Proceedings of the International Geometry Center, 9(2). https://doi.org/10.15673/tmgc.v9i2.279
Issue
Vol 9 No 2 (2016)
Section
Papers

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Author Biographies

Mariia Losieva, Taras Shevchenko National University of Kyiv

Faculty of Computer Science and Cybernetics,

Research Sector of Problems of System Analysis, Leading Engineer

Oleksandr Prishlyak, Taras Shevchenko National University of Kyiv

Geometry, Topology and dynamical systems department, professor

References

1. Fleitas G. Classification of gradient-like flows on dimensions two and three / G. Fleitas // Bulletin of Brazilian Mathematical Socienty. – 1975. – Vol. 6, Iss. 2. – P. 155–183.

2. Girik E. Classification of polar Morse-Smale vector fields on two-dimensional manifolds/ E.Girik // Meth. Funct. Anal.Topology. – 1996. – Vol. 2, №1. – P. 23–37.

3. Poltavec D. Equivalent polar Morse-Smale system on two dimensional manifolds of genus 3 / D. Poltavec // Proc. Sympose. Pure Math. – 1970. – Vol. 14. – P. 223–231.

4. Кадубовський O. Класифікація векторних полів Морса–Смейла на двовимірних многовидах / О. Кадубовський // Вісник Київського національного університету ім. Тараса Шевченка. Математика, механіка. – 2005. – Вип. 14. – С. 85–88.

5. Palis J. On Morse-Smale dynamical systems / J.Palis // Topology. – 1996. – №8. – P. 385–405.

6. Palis J. Structural stability theorems / J. Palis, S. Smale // Proc.Sympose. Pure Math. – 1970. – Vol. 14. – P. 223–231.

7. Лосева М.В. О структурно устойчивых обыкновенных дифферен-циальных уравнениях на поверхностях с краем / М.В. Лосева, А.О.Пришляк // Журнал обчисл. та приклад. математики. – 2002. – № 1(87). – C. 45–48.

8. Лосєва М.В. МС-потоки на тривимiрних многовидах з краєм / М.В. Лосєва, О.О. Пришляк // Вісник Київського національного університету ім. Тараса Шевченка. Математика, механіка. – 2006. – № 15. – С. 31–32.

9. Пришляк А.О. Топологическая классификация m-полей на двух- и трех-мерных многообразиях с краем / А.О. Пришляк // Укр.мат. журн. – 2003. – T.55, №6. – C. 799–805.

10. Labarca R. Stability of Morse-Smale vector fields on manifolds with boundary / R. Labarca, M.J. Pacifico // Topology. – 1990. – V. 29(1). – P. 57–81.

11. C. Robinson. Structural stability on manifolds with boundary / C. Robinson // Journal of Differential Equations. – 1980. – V. 37(1). – P. 1–11.