Topology of optimal flows with collective dynamics on closed orientable surfaces
We consider flows on a closed surface with one or more heteroclinic cycles that divide the surface into two regions. One of the region has gradient dynamics, like Morse fields. The other region has Hamiltonian dynamics generated by the field of the skew gradient of the simple Morse function. We cons...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2020-09-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.onaft.edu.ua/index.php/geometry/article/view/1731 |
| _version_ | 1818254442519068672 |
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| author | Alexandr Olegovich Prishlyak Mariya Viktorovna Loseva |
| author_facet | Alexandr Olegovich Prishlyak Mariya Viktorovna Loseva |
| author_sort | Alexandr Olegovich Prishlyak |
| collection | DOAJ |
| description | We consider flows on a closed surface with one or more heteroclinic cycles that divide the surface into two regions. One of the region has gradient dynamics, like Morse fields. The other region has Hamiltonian dynamics generated by the field of the skew gradient of the simple Morse function. We construct the complete topological invariant of the flow using the Reeb and Oshemkov-Shark graphs and study its properties. We describe all possible structures of optimal flows with collective dynamics on oriented surfaces of genus no more than 2, both for flows containing a center and for flows without it. |
| first_indexed | 2024-12-12T16:56:02Z |
| format | Article |
| id | doaj.art-2d3f3dc36a1e4fe7bfcf26995b219391 |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-12-12T16:56:02Z |
| publishDate | 2020-09-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-2d3f3dc36a1e4fe7bfcf26995b2193912022-12-22T00:18:13ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062020-09-01132506710.15673/tmgc.v13i2.17311731Topology of optimal flows with collective dynamics on closed orientable surfacesAlexandr Olegovich PrishlyakMariya Viktorovna LosevaWe consider flows on a closed surface with one or more heteroclinic cycles that divide the surface into two regions. One of the region has gradient dynamics, like Morse fields. The other region has Hamiltonian dynamics generated by the field of the skew gradient of the simple Morse function. We construct the complete topological invariant of the flow using the Reeb and Oshemkov-Shark graphs and study its properties. We describe all possible structures of optimal flows with collective dynamics on oriented surfaces of genus no more than 2, both for flows containing a center and for flows without it.https://journals.onaft.edu.ua/index.php/geometry/article/view/1731morse flow, topological equivalence, heteroclinic cycles, graph |
| spellingShingle | Alexandr Olegovich Prishlyak Mariya Viktorovna Loseva Topology of optimal flows with collective dynamics on closed orientable surfaces Pracì Mìžnarodnogo Geometričnogo Centru morse flow, topological equivalence, heteroclinic cycles, graph |
| title | Topology of optimal flows with collective dynamics on closed orientable surfaces |
| title_full | Topology of optimal flows with collective dynamics on closed orientable surfaces |
| title_fullStr | Topology of optimal flows with collective dynamics on closed orientable surfaces |
| title_full_unstemmed | Topology of optimal flows with collective dynamics on closed orientable surfaces |
| title_short | Topology of optimal flows with collective dynamics on closed orientable surfaces |
| title_sort | topology of optimal flows with collective dynamics on closed orientable surfaces |
| topic | morse flow, topological equivalence, heteroclinic cycles, graph |
| url | https://journals.onaft.edu.ua/index.php/geometry/article/view/1731 |
| work_keys_str_mv | AT alexandrolegovichprishlyak topologyofoptimalflowswithcollectivedynamicsonclosedorientablesurfaces AT mariyaviktorovnaloseva topologyofoptimalflowswithcollectivedynamicsonclosedorientablesurfaces |