This article is cited in 12 scientific papers (total in 12 papers)
The absence of nonclosed Poisson-stable semitrajectories and trajectories doubly asymptotic to a double limit cycle for dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds
Abstract:
In the present paper we investigate the absence, for dynamical systems of :he first degree of structural instability on two-dimensional compact orientable manifolds of any genus, of nonclosed Poisson-stable semitrajectories and trajectories that are doubly asymptotic to a double limit cycle. The propositions are some of the basic propositions that must be added to the known conditions for the first degree of structural instability on a plane (or sphere) [1] in order to obtain a description of dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds. Systems of the first degree of structural instability on a torus were considered in [2]. A study of such systems on two-dimensional manifolds of higher genus has not been carried out up to the present time.
Citation:
S. Kh. Aranson, “The absence of nonclosed Poisson-stable semitrajectories and trajectories doubly asymptotic to a double limit cycle for dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds”, Math. USSR-Sb., 5:2 (1968), 205–219
\Bibitem{Ara68}
\by S.~Kh.~Aranson
\paper The absence of nonclosed Poisson-stable semitrajectories and trajectories doubly asymptotic to a double limit cycle for dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds
\jour Math. USSR-Sb.
\yr 1968
\vol 5
\issue 2
\pages 205--219
\mathnet{http://mi.mathnet.ru/eng/sm4014}
\crossref{https://doi.org/10.1070/SM1968v005n02ABEH002593}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=226142}
\zmath{https://zbmath.org/?q=an:0179.40803|0159.11901}
Linking options:
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https://doi.org/10.1070/SM1968v005n02ABEH002593
https://www.mathnet.ru/eng/sm/v118/i2/p214
This publication is cited in the following 12 articles:
Nelson G. Markley, Mary Vanderschoot, Birkhäuser Advanced Texts Basler Lehrbücher, Flows on Compact Surfaces, 2023, 217
A. P. Afanasev, S. M. Dzyuba, “Novye svoistva rekurrentnykh dvizhenii i predelnykh mnozhestv dinamicheskikh sistem”, Vestnik rossiiskikh universitetov. Matematika, 27:137 (2022), 5–15
V. Sh. Roitenberg, “Klassifikatsiya periodicheskikh differentsialnykh uravnenii po stepenyam negrubosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 14:3 (2022), 52–59
A. P. Afanas'ev, S. M. Dzyuba, “The Interrelation of Motions of Dynamical Systems in a Metric Space”, Lobachevskii J Math, 43:12 (2022), 3414
N.G. Markley, M.H. Vanderschoot, “Remote limit points on surfaces”, Journal of Differential Equations, 188:1 (2003), 221
S. Aranson, E. Zhuzhoma, “Qualitative theory of flows on surfaces (A review)”, Journal of Mathematical Sciences (New York), 90:3 (1998), 2051
S. Kh. Aranson, E. V. Zhuzhoma, V. S. Medvedev, “On continuity of geodesic frameworks of flows on surfaces”, Sb. Math., 188:7 (1997), 955–972
S. Kh. Aranson, “On the non-denseness of fields of finite degree of non-robustness in the space of non-robust vector fields on closed two-dimensional manifolds”, Russian Math. Surveys, 43:1 (1988), 231–232
S. Kh. Aranson, V. Z. Grines, “Topological classification of flows on closed two-dimensional manifolds”, Russian Math. Surveys, 41:1 (1986), 183–208
V. S. Medvedev, “On a new type of bifurcations on manifolds”, Math. USSR-Sb., 41:3 (1982), 403–407
S. Kh. Aranson, V. Z. Grines, “On the representation of minimal sets of currents on two-dimensional manifolds by geodesics”, Math. USSR-Izv., 12:1 (1978), 103–124
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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