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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 261, Pages 115–139 (Mi tm744)  
This article is cited in 18 scientific papers (total in 18 papers)

Global Dynamics of Morse–Smale Systems

E. V. Zhuzhomaa, V. S. Medvedevb

a Nizhny Novgorod State Pedagogical University
b Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
Full-text PDF (352 kB) Citations (18)
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Abstract: This paper is a survey of relatively recent results on the classification of Morse–Smale dynamical systems on closed manifolds. It also contains both old and relatively recent results on the relationship between the topology of the ambient manifold and the dynamical characteristics of Morse–Smale systems.
Received in February 2007
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 261, Pages 112–135
DOI: https://doi.org/10.1134/S0081543808020107
Bibliographic databases:
UDC: 517.938
Language: Russian
Citation: E. V. Zhuzhoma, V. S. Medvedev, “Global Dynamics of Morse–Smale Systems”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 115–139; Proc. Steklov Inst. Math., 261 (2008), 112–135
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tm744
  • https://www.mathnet.ru/eng/tm/v261/p115
    • This publication is cited in the following 18 articles:
    1. Vladislav S. Medvedev, Evgeny V. Zhuzhoma, “Smale Regular and Chaotic A-Homeomorphisms and A-Diffeomorphisms”, Regul. Chaotic Dyn., 28:2 (2023), 131–147  mathnet  crossref  mathscinet
    2. Leandro Ayarde-Henríquez, Cristian Guerra, Mario Duque-Noreña, Eduardo Chamorro, “A simple topology-based model for predicting the activation barriers of reactive processes at 0 K”, Phys. Chem. Chem. Phys., 25:20 (2023), 14274  crossref
    3. E. V. Zhuzhoma, V. S. Medvedev, “Many-Dimensional Morse–Smale Diffeomeophisms with a Dominant Saddle”, Math. Notes, 111:6 (2022), 870–878  mathnet  crossref  crossref  mathscinet
    4. Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma, “On the Topological Structure of Manifolds Supporting Axiom A Systems”, Regul. Chaotic Dyn., 27:6 (2022), 613–628  mathnet  crossref  mathscinet
    5. V. Medvedev, E. Zhuzhoma, “High-dimensional Morse-Smale systems with king-saddles”, Topology and its Applications, 312 (2022), 108080  crossref
    6. E. V. Zhuzhoma, V. S. Medvedev, “Necessary and sufficient conditions for the conjugacy of Smale regular homeomorphisms”, Sb. Math., 212:1 (2021), 57–69  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. E. V. Zhuzhoma, V. S. Medvedev, “Underlying Manifolds of High-Dimensional Morse–Smale Diffeomorphisms with Two Saddle Periodic Points”, Math. Notes, 109:3 (2021), 398–404  mathnet  crossref  crossref  mathscinet  isi
    8. Medvedev V. Zhuzhoma E., “Supporting Manifolds For High-Dimensional Morse-Smale Diffeomorphisms With Few Saddles”, Topology Appl., 282 (2020), 107315  crossref  mathscinet  isi
    9. E. V. Zhuzhoma, V. S. Medvedev, “Conjugacy of Morse–Smale Diffeomorphisms with Three Nonwandering Points”, Math. Notes, 104:5 (2018), 753–757  mathnet  crossref  crossref  mathscinet  isi  elib
    10. V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “On the structure of the ambient manifold for Morse–Smale systems without heteroclinic intersections”, Proc. Steklov Inst. Math., 297 (2017), 179–187  mathnet  crossref  crossref  mathscinet  isi  elib
    11. E. V. Zhuzhoma, V. S. Medvedev, “Continuous Morse-Smale flows with three equilibrium positions”, Sb. Math., 207:5 (2016), 702–723  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. V. Z. Grines, E. V. Zhuzhoma, S. V. Medvedev, N. A. Tarasova, “O suschestvovanii periodicheskikh traektorii dlya nepreryvnykh potokov Morsa-Smeila”, Zhurnal SVMO, 18:1 (2016), 12–16  mathnet  elib
    13. Grines V. Pochinka O. Zhuzhoma E., “on Families of Diffeomorphisms With Bifurcations of Attractive and Repelling Sets”, Int. J. Bifurcation Chaos, 24:8 (2014), 1440015  crossref  mathscinet  zmath  isi  elib  scopus
    14. Medvedev V.S. Zhuzhoma E.V., “Morse-Smale Systems with Few Non-Wandering Points”, Topology Appl., 160:3 (2013), 498–507  crossref  mathscinet  zmath  isi  elib  scopus
    15. Medvedev V.S. Zhuzhoma E.V., “Locally Flat and Wildly Embedded Separatrices in Simplest Morse-Smale Systems”, J. Dyn. Control Syst., 18:3 (2012), 433–448  crossref  mathscinet  zmath  isi  elib  scopus
    16. Zhuzhoma E.V., Medvedev V.S., “Morse-Smale systems with three nonwandering points”, Dokl. Math., 84:2 (2011), 604–606  crossref  mathscinet  zmath  isi  elib  elib  scopus
    17. Viacheslav Grines, Evgeny Zhuzhoma, Springer Proceedings in Mathematics, 1, Dynamics, Games and Science I, 2011, 421  crossref
    18. V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, O. V. Pochinka, “Global attractor and repeller of Morse–Smale diffeomorphisms”, Proc. Steklov Inst. Math., 271 (2010), 103–124  mathnet  crossref  mathscinet  isi  elib
    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
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