The simplest nonsingular flows on closed orientable 3-manifolds are studied. We establish that each class of topological equivalence of the simplest nonsingular flow on a lens consists of an infinite set of topological conjugacy classes. We obtain necessary and sufficient conditions for the topological conjugacy of the flows under consideration.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Campos, A. Cordero, J. Martinez-Alfaro, and P. Vindel, “NMS flows on three-dimensional manifolds with one saddle periodic orbit,” Acta Math. Sin., Engl. Ser. 20, No. 1, 47–56 (2004).
A. L. Dobrolyubova and V. E. Kruglov, “Topological conjugacy of non-singular flows with two limit cycles on S2 ×S1” [in Russian], Zh. Sredn. Mat. Obshch. 24, No. 1, 40–53 (2022).
M. C. Irwin, “A classification of elementary cycles,” Topology 9, 35–47 (1970).
O. V. Pochinka and D. D. Shubin, “Non-singular Morse–Smale flows on n-manifolds with attractor-repeller dynamics,” Nonlinearity 35, No. 3, 1485–1499 (2022).
S. Smale, “Differentiable dynamical systems,” Bull. Am. Math. Soc. 73, No. 6, 747–817 (1967).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Problemy Matematicheskogo Analiza 121, 2023, pp. 35-42.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Dobrolyubova, A.L., Kruglov, V.E. & Pochinka, O.V. Topological Conjugacy of the Simplest Nonsingular Three-Dimensional Flows. J Math Sci 269, 165–172 (2023). https://doi.org/10.1007/s10958-023-06267-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06267-7