Topological conjugacy of 𝑛-multiple Cartesian products of circle rough transformations
Open Access
- 30 November 2021
- journal article
- research article
- Published by Saratov State University in Izvestiya VUZ. Applied Nonlinear Dynamics
- Vol. 29 (6), 851-862
- https://doi.org/10.18500/0869-6632-2021-29-6-851-862
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- Dynamical Systems on 2- and 3-ManifoldsPublished by Springer Science and Business Media LLC ,2016