|
This article is cited in 1 scientific paper (total in 1 paper)
BIFURCATION IN DYNAMICAL SYSTEMS. DETERMINISTIC CHAOS. QUANTUM CHAOS.
Topological conjugacy of n-multiple Cartesian products of circle rough transformations
I. V. Golikovaa, S. Kh. Zininab a National Research University
“Higher School of Economics”, Nizhny Novgorod, Russia
b Mordovia State University, Saransk, Russia
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:
Morse - Smale diffeomorphisms, circle rough transformations, rotation number, periodic orbits, topological invariants.
Received: 28.05.2021
Citation:
I. V. Golikova, S. Kh. Zinina, “Topological conjugacy of n-multiple Cartesian products of circle rough transformations”, Izvestiya VUZ. Applied Nonlinear Dynamics, 29:6 (2021), 851–862
Linking options:
https://www.mathnet.ru/eng/ivp451 https://www.mathnet.ru/eng/ivp/v29/i6/p851
|
Statistics & downloads: |
Abstract page: | 79 | Full-text PDF : | 36 |
|