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Moscow Mathematical Journal, 2019, Volume 19, Number 4, Pages 739–760
DOI: https://doi.org/10.17323/1609-4514-2019-19-4-739-760
(Mi mmj751)
 

This article is cited in 5 scientific papers (total in 5 papers)

On embedding of multidimensional Morse–Smale diffeomorphisms into topological flows

V. Grines, E. Gurevich, O. Pochinka

National Research University Higher School of Economics Nizhnii Novgorod, B. Pechorskaya str., 25, 224
Full-text PDF Citations (5)
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Abstract: J. Palis found necessary conditions for a Morse–Smale diffeomorphism on a closed $n$-dimensional manifold $M^n$ to embed into a topological flow and proved that these conditions are also sufficient for $n=2$. For the case $n=3$ a possibility of wild embedding of closures of separatrices of saddles is an additional obstacle for Morse–Smale cascades to embed into topological flows. In this paper we show that there are no such obstructions for Morse–Smale diffeomorphisms without heteroclinic intersection given on the sphere $S^n$, $n\geq 4$, and Palis conditions again are sufficient for such diffeomorphisms.
Key words and phrases: Morse–Smale dynamical systems, embedding in topological flows, topological classification.
Funding agency Grant number
Russian Science Foundation 17-11-01041
HSE Basic Research Program
Research is done with financial support of Russian Science Foundation (project 17-11-01041) except Section 4.3, which is done in the framework of the Basic Research Program of HSE in 2019.
Bibliographic databases:
Document Type: Article
MSC: 37D15
Language: English
Citation: V. Grines, E. Gurevich, O. Pochinka, “On embedding of multidimensional Morse–Smale diffeomorphisms into topological flows”, Mosc. Math. J., 19:4 (2019), 739–760
Citation in format AMSBIB
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\paper On embedding of multidimensional Morse--Smale diffeomorphisms into topological flows
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\vol 19
\issue 4
\pages 739--760
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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