Abstract:
We consider the class G(Sn) of orientation-preserving Morse–Smale diffeomorphisms defined on the sphere Sn of dimension n≥4 under the assumption that the invariant manifolds of different saddle periodic points are disjoint. For diffeomorphisms in this class, we describe an algorithm for constructing representatives of all topological conjugacy classes.
This work is supported by the Russian Science Foundation under grant 17-11-01041, except for the proof of Lemma 1. The work on the proof of Lemma 1 is supported by the HSE Laboratory of Dynamical Systems and Applications and the Ministry of Science and Higher Education of the Russian Federation under grant 075-15-2019-1931.
Citation:
V. Z. Grines, E. Ya. Gurevich, V. S. Medvedev, “On Realization of Topological Conjugacy Classes of Morse–Smale Cascades on the Sphere Sn”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 119–134; Proc. Steklov Inst. Math., 310 (2020), 108–123
\Bibitem{GriGurMed20}
\by V.~Z.~Grines, E.~Ya.~Gurevich, V.~S.~Medvedev
\paper On Realization of Topological Conjugacy Classes of Morse--Smale Cascades on the Sphere $S^n$
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 310
\pages 119--134
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4096}
\crossref{https://doi.org/10.4213/tm4096}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4173194}
\elib{https://elibrary.ru/item.asp?id=45107133}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2020
\vol 310
\pages 108--123
\crossref{https://doi.org/10.1134/S0081543820050089}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000595790500008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85097083068}
Linking options:
https://www.mathnet.ru/eng/tm4096
https://doi.org/10.4213/tm4096
https://www.mathnet.ru/eng/tm/v310/p119
This publication is cited in the following 3 articles:
V. Z. Grines, E. Ya. Gurevich, “A combinatorial invariant of gradient-like flows on a connected sum of $\mathbb{S}^{n-1}\times\mathbb{S}^1$”, Sb. Math., 214:5 (2023), 703–731
V. Z. Grines, E. Ya. Gurevich, “On classification of Morse–Smale flows on projective-like manifolds”, Izv. Math., 86:5 (2022), 876–902
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
Citation in format AMSBIB
Contact us: