This article is cited in 41 scientific papers (total in 41 papers)
On some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems)
Abstract:
In this paper, topological invariants of dynamical systems given on a two-dimensional manifold $M^2$ of genus $p>1$ are selected which allow one to distinguish topologically inequivalent systems which have nonclosed, Poisson stable trajectories and non-null-homotopic closed trajectories.
A necessary and sufficient condition for the topological equivalence of transitive dynamical systems on $M^2$ is established.
Figures: 6.
Bibliography: 20 titles.
Citation:
S. Kh. Aranson, V. Z. Grines, “On some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems)”, Math. USSR-Sb., 19:3 (1973), 365–393
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\paper On~some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems)
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 3
\pages 365--393
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\crossref{https://doi.org/10.1070/SM1973v019n03ABEH001784}
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\zmath{https://zbmath.org/?q=an:0252.54027}
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This publication is cited in the following 41 articles:
Nelson G. Markley, Mary Vanderschoot, Birkhäuser Advanced Texts Basler Lehrbücher, Flows on Compact Surfaces, 2023, 217
V. Z. Grines, E. D. Kurenkov, “Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets”, Izv. Math., 84:5 (2020), 862–909
V. Z. Grines, E. D. Kurenkov, “Predstavlenie prostorno raspolozhennykh sovershennykh attraktorov diffeomorfizmov geodezicheskimi laminatsiyami”, Zhurnal SVMO, 20:2 (2018), 159–174
Grines V., Zhuzhoma E., “Around Anosov-Weil Theory”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. Katok A., Pesin Y., Hertz F., Amer Mathematical Soc, 2017, 123–154
N. V. Isaenkova, E. V. Zhuzhoma, “Sopryazhenie diffeomorfizmov Smeila-Vietorisa posredstvom sopryazheniya endomorfizmov”, Zhurnal SVMO, 19:1 (2017), 38–50
Maksymenko S., Polulyakh E., “Foliations With All Non-Closed Leaves on Non-Compact Surfaces”, Methods Funct. Anal. Topol., 22:3 (2016), 266–282
Alexander Bufetov, “Limit theorems for translation flows”, Ann. Math, 179:2 (2013), 431
Budnyts'ka N.V., Rybalkina T.V., “Realization of a Closed 1-Form on Closed Oriented Surfaces”, Ukr. Math. J., 64:6 (2012), 844–856
Medvedev T.V., “Klassifikatsiya potokov tipa cherri na neorientiruemoi poverkhnosti roda tri”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2011, no. 2, 139–145
Medvedev T.V., “Klassifikatsiya potokov tipa cherri na neorientiruemoi poverkhnosti roda tri”, Vestnik nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2011, no. 2-1, 139–145
Viacheslav Grines, Evgeny Zhuzhoma, Springer Proceedings in Mathematics, 1, Dynamics, Games and Science I, 2011, 421
N. Markley, M. Vanderschoot, “Recurrent orbits for flows on surfaces”, Journal of Differential Equations, 244:5 (2008), 1210
S. Kh. Aranson, I. A. Gorelikova, E. V. Zhuzhoma, “Closed cross-sections of irrational flows on surfaces”, Sb. Math., 197:2 (2006), 173–192
D. V. Anosov, E. V. Zhuzhoma, “Nonlocal asymptotic behavior of curves and leaves of laminations on universal coverings”, Proc. Steklov Inst. Math., 249 (2005), 1–221
E. V. Zhuzhoma, “Continuous Dependence of Geodesic Frames in the Hausdorff Metric”, Math. Notes, 77:6 (2005), 862–864
S. Kh. Aranson, E. V. Zhuzhoma, “Nonlocal Properties of Analytic Flows on Closed Orientable Surfaces”, Proc. Steklov Inst. Math., 244 (2004), 2–17
N.G. Markley, M.H. Vanderschoot, “Remote limit points on surfaces”, Journal of Differential Equations, 188:1 (2003), 221
Aranson S. Grines V. Kaimanovich V., “Classification of Supertransitive 2-Webs on Surfaces”, J. Dyn. Control Syst., 9:4 (2003), 455–468
D. V. Anosov, E. V. Zhuzhoma, “Asymptotic Behavior of Covering Curves on the Universal Coverings of Surfaces”, Proc. Steklov Inst. Math., 238 (2002), 1–46
S. Aranson, V. Grines, E. Zhuzhoma, “On Anosov–Weil problem”, Topology, 40:3 (2001), 475
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