Topological conjugacy of n-multiple Cartesian products of circle rough transformations
| Autor: | Golikova, Iuliana Viktorovna, Zinina, Svetlana Halilovna |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Известия высших учебных заведений: Прикладная нелинейная динамика, Vol 29, Iss 6, Pp 851-862 (2021) |
| Druh dokumentu: | article |
| ISSN: | 0869-6632 2542-1905 |
| DOI: | 10.18500/0869-6632-2021-29-6-851-862 |
| Popis: | It is known from the 1939 work of A. G. Mayer that rough transformations of the circle are limited to the diffeomorphisms of Morse – Smale. A topological conjugacy class of orientation-preserving diffeomorphism is entirely determined by its rotation number and the number of its periodic orbits, while for orientation-changing diffeomorphism the topological invariant will be only the number of periodic orbits. Thus, the purpose of this study is to find topological invariants of n-fold Cartesian products of diffeomorphisms of a circle. Methods. This paper explores the rough Morse – Smale diffeomorphisms on the n-torus surface. To prove the main result, additional constructions and formation of subsets of considered sets were used. Results. In this paper, a numerical topological invariant is introduced for n-fold Cartesian products of rough circle transformations. Conclusion.The criterion of topological conjugacy of n-fold Cartesian products of rough transformations of a circle is formulated. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|