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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| Format: | Article |
| Language: | English |
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Saratov State University
2021-11-01
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| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
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| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2021/11/golikova-zinina_851-862_2.pdf |
| _version_ | 1818573885005627392 |
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| author | Golikova, Iuliana Viktorovna Zinina, Svetlana Halilovna |
| author_facet | Golikova, Iuliana Viktorovna Zinina, Svetlana Halilovna |
| author_sort | Golikova, Iuliana Viktorovna |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-15T00:18:52Z |
| format | Article |
| id | doaj.art-f1119450b0c64724a98a82e59c589215 |
| institution | Directory Open Access Journal |
| issn | 0869-6632 2542-1905 |
| language | English |
| last_indexed | 2024-12-15T00:18:52Z |
| publishDate | 2021-11-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj.art-f1119450b0c64724a98a82e59c5892152022-12-21T22:42:22ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052021-11-0129685186210.18500/0869-6632-2021-29-6-851-862Topological conjugacy of n-multiple Cartesian products of circle rough transformationsGolikova, Iuliana Viktorovna0Zinina, Svetlana Halilovna1National Research University "Higher School of Economics", ul. Myasnitskaya 20, Moscow, 101000, RussiaMordovia State University, st. Bolshevistskya, 68, Saransk, Republic of Mordovia, 430005It 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.https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2021/11/golikova-zinina_851-862_2.pdfmorse – smale diffeomorphismscircle rough transformationsrotation numberperiodic orbitstopological invariants |
| spellingShingle | Golikova, Iuliana Viktorovna Zinina, Svetlana Halilovna Topological conjugacy of n-multiple Cartesian products of circle rough transformations Известия высших учебных заведений: Прикладная нелинейная динамика morse – smale diffeomorphisms circle rough transformations rotation number periodic orbits topological invariants |
| title | 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_short | Topological conjugacy of n-multiple Cartesian products of circle rough transformations |
| title_sort | topological conjugacy of n multiple cartesian products of circle rough transformations |
| topic | morse – smale diffeomorphisms circle rough transformations rotation number periodic orbits topological invariants |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2021/11/golikova-zinina_851-862_2.pdf |
| work_keys_str_mv | AT golikovaiulianaviktorovna topologicalconjugacyofnmultiplecartesianproductsofcircleroughtransformations AT zininasvetlanahalilovna topologicalconjugacyofnmultiplecartesianproductsofcircleroughtransformations |