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Tr. Mat. Inst. Steklova, 2017, Volume 297, Pages 201–210 (Mi tm3800)  

This article is cited in 2 scientific papers (total in 2 papers)

On the structure of the ambient manifold for Morse–Smale systems without heteroclinic intersections

V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev

National Research University "Higher School of Economics", ul. Myasnitskaya 20, Moscow, 101000 Russia

Abstract: It is shown that if a closed smooth orientable manifold $M^n$, $n\geq3$, admits a Morse–Smale system without heteroclinic intersections (the absence of periodic trajectories is additionally required in the case of a Morse–Smale flow), then this manifold is homeomorphic to the connected sum of manifolds whose structure is interconnected with the type and number of points that belong to the non-wandering set of the Morse–Smale system.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03689-а
16-51-10005-Ko_a
Russian Science Foundation 14-41-00044
HSE Basic Research Program 90
This work is supported by the Russian Foundation for Basic Research (project nos. 15-01-03689‑a and 16-51-10005-Ko_a) and by the Russian Science Foundation (project no. 14-41-00044). The research is carried out within the HSE Basic Research Program (project no. 90) in 2017.


DOI: https://doi.org/10.1134/S0371968517020108

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 297, 179–187

Bibliographic databases:

UDC: 517.938
Received: April 3, 2017

Citation: V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “On the structure of the ambient manifold for Morse–Smale systems without heteroclinic intersections”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Tr. Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 201–210; Proc. Steklov Inst. Math., 297 (2017), 179–187

Citation in format AMSBIB
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\paper On the structure of the ambient manifold for Morse--Smale systems without heteroclinic intersections
\inbook Order and chaos in dynamical systems
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov
\serial Tr. Mat. Inst. Steklova
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\vol 297
\pages 201--210
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, E. Ya. Gurevich, “O topologii mnogoobrazii, dopuskayuschikh gradientno-podobnye potoki s zadannym nebluzhdayuschim mnozhestvom”, Matem. tr., 21:2 (2018), 163–180  mathnet  crossref
    2. 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  mathnet  crossref  crossref  adsnasa  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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