V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “Classification of Morse–Smale diffeomorphisms with one-dimensional set of unstable separatrices”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 62–85; Proc. Steklov Inst. Math., 270 (2010), 57

Trudy Matematicheskogo Instituta imeni V.A. Steklova

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 270, Pages 62–85 (Mi tm3025)

This article is cited in 18 scientific papers (total in 18 papers)

Classification of Morse–Smale diffeomorphisms with one-dimensional set of unstable separatrices

V. Z. Grines^a, E. Ya. Gurevich^a, V. S. Medvedev^b

^a Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
^b Research Institute for Applied Mathematics and Cybernetics, Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia

Full-text PDF (427 kB) Citations (18)

References:

PDF

HTML

Abstract: Let

$M^n$ be a closed orientable manifold of dimension

$n>3$ . We study the class

$G_1(M^n)$ of orientation-preserving Morse–Smale diffeomorphisms of

$M^n$ such that the set of unstable separatrices of any

$f\in G_1(M^n)$ is one-dimensional and does not contain heteroclinic intersections. We prove that the Peixoto graph (equipped with an automorphism) is a complete topological invariant for diffeomorphisms of class

$G_1(M^n)$ , and construct a standard representative for any class of topologically conjugate diffeomorphisms.

Received in April 2009

English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 270, Pages 57–79
DOI: https://doi.org/10.1134/S0081543810030053

Bibliographic databases:

Document Type: Article

UDC: 517.938

Language: Russian

Citation: V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “Classification of Morse–Smale diffeomorphisms with one-dimensional set of unstable separatrices”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 62–85; Proc. Steklov Inst. Math., 270 (2010), 57–79

Citation in format AMSBIB

\Bibitem{GriGurMed10}

\by V.~Z.~Grines, E.~Ya.~Gurevich, V.~S.~Medvedev

\paper Classification of Morse--Smale diffeomorphisms with one-dimensional set of unstable separatrices

\inbook Differential equations and dynamical systems

\bookinfo Collected papers

\serial Trudy Mat. Inst. Steklova

\yr 2010

\vol 270

\pages 62--85

\publ MAIK Nauka/Interperiodica

\publaddr Moscow

\mathnet{http://mi.mathnet.ru/tm3025}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2768937}

\zmath{https://zbmath.org/?q=an:1226.37012}

\elib{https://elibrary.ru/item.asp?id=15249750}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2010

\vol 270

\pages 57--79

\crossref{https://doi.org/10.1134/S0081543810030053}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000282431700005}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77957372637}

Linking options:

https://www.mathnet.ru/eng/tm3025

https://www.mathnet.ru/eng/tm/v270/p62

This publication is cited in the following 18 articles:

V. Medvedev, E. Zhuzhoma, “High-dimensional Morse-Smale systems with king-saddles”, Topology and its Applications, 312 (2022), 108080
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. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “On Realization of Topological Conjugacy Classes of Morse–Smale Cascades on the Sphere $S^n$ ”, 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
Vladislav E. Kruglov, Dmitry S. Malyshev, Olga V. Pochinka, Danila D. Shubin, “On Topological Classification of Gradient-like Flows on an $n$ -sphere in the Sense of Topological Conjugacy”, Regul. Chaotic Dyn., 25:6 (2020), 716–728
Grines V. Gurevich E. Pochinka O. Malyshev D., “On Topological Classification of Morse-Smale Diffeomorphisms on the Sphere S-N (N > 3)”, Nonlinearity, 33:12 (2020), 7088–7113
V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “A Combinatorial Invariant of Morse–Smale Diffeomorphisms without Heteroclinic Intersections on the Sphere $S^n$ , $n\ge 4$ ”, Math. Notes, 105:1 (2019), 132–136
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
Pochinka V O., Galkina S.Yu., Shubin D.D., “Modeling of Gradient-Like Flows on N-Sphere”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 27:6 (2019), 63–72
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
E. V. Nozdrinova, “Suschestvovanie svyaznogo kharakteristicheskogo prostranstva u gradientno-podobnykh diffeomorfizmov poverkhnostei”, Zhurnal SVMO, 19:2 (2017), 91–97
Vyacheslav Z. Grines, Dmitry S. Malyshev, Olga V. Pochinka, Svetlana Kh. Zinina, “Efficient Algorithms for the Recognition of Topologically Conjugate Gradient-like Diffeomorhisms”, Regul. Chaotic Dyn., 21:2 (2016), 189–203
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
E. Ya. Gurevich, D. S. Malyshev, “O topologicheskoi klassifikatsii diffeomorfizmov Morsa-Smeila na sfere $S^n$ posredstvom raskrashennogo grafa”, Zhurnal SVMO, 18:4 (2016), 30–33
V. Z. Grines, E. A. Gurevich, O. V. Pochinka, “Topological Classification of Morse–Smale Diffeomorphisms Without Heteroclinic Intersections”, J Math Sci, 208:1 (2015), 81
V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “Embedding in a Flow of Morse–Smale Diffeomorphisms on Manifolds of Dimension Higher than Two”, Math. Notes, 91:5 (2012), 742–745
V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, O. V. Pochinka, “On embedding a Morse-Smale diffeomorphism on a 3-manifold in a topological flow”, Sb. Math., 203:12 (2012), 1761–1784

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

Statistics & downloads:
Abstract page:	483
Full-text PDF :	199
References:	104

Что такое QR-код?

Registration to the website

Logotypes