On functional moduli of surface flows
Currently, an complete topological classification has been obtained with respect to the topological equivalence of Morse-Smale flows, [9, 7], as well as their generalizations of Ω-stable flows on closed surfaces, [4]. Some results on topological conjugacy classification for such systems are also kno...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Odesa National University of Technology
2020-06-01
|
| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.onaft.edu.ua/index.php/geometry/article/view/1714 |
| _version_ | 1811326871308075008 |
|---|---|
| author | Vladislav Kruglov Olga Pochinka Galina Talanova |
| author_facet | Vladislav Kruglov Olga Pochinka Galina Talanova |
| author_sort | Vladislav Kruglov |
| collection | DOAJ |
| description | Currently, an complete topological classification has been obtained with respect to the topological equivalence of Morse-Smale flows, [9, 7], as well as their generalizations of Ω-stable flows on closed surfaces, [4]. Some results on topological conjugacy classification for such systems are also known. In particular, the coincidence of the classes of topological equivalence and conjugacy of gradient-like flows (Morse-Smale flows without periodic orbits) was established in [3]. In the classical paper [8], it was proved that in the presence of connections (coincidence of saddle separatrices), the topological equivalence class of a Ω-stable flow splits into a continuum of topological conjugacy classes (has moduli). Obviously, each periodic orbit also generates at least one modulus associated with the period of that orbit. In the present work, it was established that the presence of a cell in a flow bounded by two limit cycles leads to the existence of an infinitely many stability moduli. In addition, a criterion for the topological conjugation of flows on such cells was found. |
| first_indexed | 2024-04-13T14:57:00Z |
| format | Article |
| id | doaj.art-4b0ec2b71633420dbfe6b0b7596abbfb |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-04-13T14:57:00Z |
| publishDate | 2020-06-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-4b0ec2b71633420dbfe6b0b7596abbfb2022-12-22T02:42:24ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062020-06-01131496010.15673/tmgc.v13i1.17141714On functional moduli of surface flowsVladislav Kruglov0Olga Pochinka1Galina Talanova2National Research University Higher School of EconomicsNational Research University Higher School of Economics, Russian FederationNational Research University Higher School of Economics, Russian FederationCurrently, an complete topological classification has been obtained with respect to the topological equivalence of Morse-Smale flows, [9, 7], as well as their generalizations of Ω-stable flows on closed surfaces, [4]. Some results on topological conjugacy classification for such systems are also known. In particular, the coincidence of the classes of topological equivalence and conjugacy of gradient-like flows (Morse-Smale flows without periodic orbits) was established in [3]. In the classical paper [8], it was proved that in the presence of connections (coincidence of saddle separatrices), the topological equivalence class of a Ω-stable flow splits into a continuum of topological conjugacy classes (has moduli). Obviously, each periodic orbit also generates at least one modulus associated with the period of that orbit. In the present work, it was established that the presence of a cell in a flow bounded by two limit cycles leads to the existence of an infinitely many stability moduli. In addition, a criterion for the topological conjugation of flows on such cells was found.https://journals.onaft.edu.ua/index.php/geometry/article/view/1714non-singular flow, morse-smale flow, conjugacy, equivalence, limit cycle |
| spellingShingle | Vladislav Kruglov Olga Pochinka Galina Talanova On functional moduli of surface flows Pracì Mìžnarodnogo Geometričnogo Centru non-singular flow, morse-smale flow, conjugacy, equivalence, limit cycle |
| title | On functional moduli of surface flows |
| title_full | On functional moduli of surface flows |
| title_fullStr | On functional moduli of surface flows |
| title_full_unstemmed | On functional moduli of surface flows |
| title_short | On functional moduli of surface flows |
| title_sort | on functional moduli of surface flows |
| topic | non-singular flow, morse-smale flow, conjugacy, equivalence, limit cycle |
| url | https://journals.onaft.edu.ua/index.php/geometry/article/view/1714 |
| work_keys_str_mv | AT vladislavkruglov onfunctionalmoduliofsurfaceflows AT olgapochinka onfunctionalmoduliofsurfaceflows AT galinatalanova onfunctionalmoduliofsurfaceflows |