Topological conjugacy of n-multiple Cartesian products of circle rough transformations

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 or...

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Autores principales:	Golikova, Iuliana Viktorovna, Zinina, Svetlana Halilovna
Formato:	article
Lenguaje:	EN RU
Publicado:	Saratov State University 2021
Materias:	morse – smale diffeomorphisms circle rough transformations rotation number periodic orbits topological invariants Physics QC1-999
Acceso en línea:	https://doaj.org/article/f1119450b0c64724a98a82e59c589215
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spelling	oai:doaj.org-article:f1119450b0c64724a98a82e59c5892152021-11-30T10:44:49ZTopological conjugacy of n-multiple Cartesian products of circle rough transformations0869-66322542-190510.18500/0869-6632-2021-29-6-851-862https://doaj.org/article/f1119450b0c64724a98a82e59c5892152021-11-01T00:00:00Zhttps://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2021/11/golikova-zinina_851-862_2.pdfhttps://doaj.org/toc/0869-6632https://doaj.org/toc/2542-1905It 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.Golikova, Iuliana ViktorovnaZinina, Svetlana HalilovnaSaratov State Universityarticlemorse – smale diffeomorphismscircle rough transformationsrotation numberperiodic orbitstopological invariantsPhysicsQC1-999ENRUИзвестия высших учебных заведений: Прикладная нелинейная динамика, Vol 29, Iss 6, Pp 851-862 (2021)
institution	DOAJ
collection	DOAJ
language	EN RU
topic	morse – smale diffeomorphisms circle rough transformations rotation number periodic orbits topological invariants Physics QC1-999
spellingShingle	morse – smale diffeomorphisms circle rough transformations rotation number periodic orbits topological invariants Physics QC1-999 Golikova, Iuliana Viktorovna Zinina, Svetlana Halilovna Topological conjugacy of n-multiple Cartesian products of circle rough transformations
description	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.
format	article
author	Golikova, Iuliana Viktorovna Zinina, Svetlana Halilovna
author_facet	Golikova, Iuliana Viktorovna Zinina, Svetlana Halilovna
author_sort	Golikova, Iuliana Viktorovna
title	Topological conjugacy of n-multiple Cartesian products of circle rough transformations
title_short	Topological conjugacy of n-multiple Cartesian products of circle rough transformations
title_full	Topological conjugacy of n-multiple Cartesian products of circle rough transformations
title_fullStr	Topological conjugacy of n-multiple Cartesian products of circle rough transformations
title_full_unstemmed	Topological conjugacy of n-multiple Cartesian products of circle rough transformations
title_sort	topological conjugacy of n-multiple cartesian products of circle rough transformations
publisher	Saratov State University
publishDate	2021
url	https://doaj.org/article/f1119450b0c64724a98a82e59c589215
work_keys_str_mv	AT golikovaiulianaviktorovna topologicalconjugacyofnmultiplecartesianproductsofcircleroughtransformations AT zininasvetlanahalilovna topologicalconjugacyofnmultiplecartesianproductsofcircleroughtransformations
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Topological conjugacy of n-multiple Cartesian products of circle rough transformations

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