Аннотация:
In this paper, following J. Nielsen, we introduce a complete characteristic of orientation-
preserving periodic maps on the two-dimensional torus. All admissible complete characteristics
were found and realized. In particular, each of the classes of orientation-preserving periodic
homeomorphisms on the 2-torus that are nonhomotopic to the identity is realized by an algebraic
automorphism. Moreover, it is shown that the number of such classes is finite. According to
V. Z. Grines and A. Bezdenezhnykh, any gradient-like orientation-preserving diffeomorphism of
an orientable surface is represented as a superposition of the time-1 map of a gradient-like flow
and some periodic homeomorphism. Thus, the results of this work are directly related to the
complete topological classification of gradient-like diffeomorphisms on surfaces.
Ключевые слова:
gradient-like flows and diffeomorphisms on surfaces, periodic homeomorphisms,
torus.
Финансовая поддержка
Номер гранта
Научный фонд НИУ ВШЭ
21-04-004
The publication was prepared within the framework of the Academic Fund Program at the HSE University
in 2021-2022 (grant 21-04-004).
Поступила в редакцию: 10.04.2022 Принята в печать: 10.06.2022
Образец цитирования:
D. A. Baranov, V. Z. Grines, O. V. Pochinka, E. E. Chilina, “On a Classification of Periodic Maps on the 2-Torus”, Rus. J. Nonlin. Dyn., 19:1 (2023), 91–110
\RBibitem{BarGriPoc23}
\by D. A. Baranov, V. Z. Grines, O. V. Pochinka, E. E. Chilina
\paper On a Classification of Periodic Maps on the 2-Torus
\jour Rus. J. Nonlin. Dyn.
\yr 2023
\vol 19
\issue 1
\pages 91--110
\mathnet{http://mi.mathnet.ru/nd840}
\crossref{https://doi.org/10.20537/nd220702}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4573514}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nd840
https://www.mathnet.ru/rus/nd/v19/i1/p91
Эта публикация цитируется в следующих 1 статьяx:
A.A. Nozdrinov, E.V. Nozdrinova, O.V. Pochinka, “Stable isotopy connectivity of gradient-like diffeomorphisms of 2-torus”, Journal of Geometry and Physics, 2024, 105352
Цитирование в формате AMSBIB
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