|
Mathematical problems of nonlinearity
The Topological Classification of Diffeomorphisms of the Two-Dimensional Torus with an Orientable Attractor
V. Z. Grinesa, E. V. Kruglovb, O. V. Pochinkaa a National Research University Higher School of Economics,
ul. B. Pecherskaya 25/12, Nizhny Novgorod, 603150 Russia
b Lobachevsky State University of Nizhny Novgorod,
prosp. Gagarina 23, Nizhny Novgorod, 603950 Russia
Аннотация:
This paper is devoted to the topological classification of structurally stable diffeomorphisms of the two-dimensional torus whose nonwandering set consists of an orientable one-dimensional attractor and finitely many isolated source and saddle periodic points, under the assumption that the closure of the union of the stable manifolds of isolated periodic points consists of simple pairwise nonintersecting arcs. The classification of one-dimensional basis sets on surfaces has been exhaustively obtained in papers by V. Grines. He also obtained a classification of some classes of structurally stable diffeomorphisms of surfaces using combined algebra-geometric invariants. In this paper, we distinguish a class of diffeomorphisms that admit purely algebraic differentiating invariants.
Ключевые слова:
A-diffeomorphisms of a torus, topological classification, orientable attractor.
Поступила в редакцию: 30.11.2020 Принята в печать: 14.12.2020
Образец цитирования:
V. Z. Grines, E. V. Kruglov, O. V. Pochinka, “The Topological Classification of Diffeomorphisms of the Two-Dimensional Torus with an Orientable Attractor”, Rus. J. Nonlin. Dyn., 16:4 (2020), 595–606
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nd731 https://www.mathnet.ru/rus/nd/v16/i4/p595
|
Статистика просмотров: |
Страница аннотации: | 146 | PDF полного текста: | 73 | Список литературы: | 13 |
|