Regular and Chaotic Dynamics
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Regul. Chaotic Dyn., 2021, том 26, выпуск 4, страницы 350–369 (Mi rcd1120)  

Construction of the Morse –Bott Energy Function for Regular Topological Flows

Olga V. Pochinkaa, Svetlana Kh. Zininab

a National Research University Higher School of Economics, ul. Bolshaya Pecherskaya 25/12, 603155 Nizhny Novgorod, Russia
b National Research Mordovian State University, ul. Bolshevistskaya 68/1, 430003 Saransk, Russia

Аннотация: In this paper, we consider regular topological flows on closed n-manifolds. Such flows have a hyperbolic (in the topological sense) chain recurrent set consisting of a finite number of fixed points and periodic orbits. The class of such flows includes, for example, Morse – Smale flows, which are closely related to the topology of the supporting manifold. This connection is provided by the existence of the Morse – Bott energy function for the Morse – Smale flows. It is well known that, starting from dimension 4, there exist nonsmoothing topological manifolds, on which dynamical systems can be considered only in a continuous category. The existence of continuous analogs of regular flows on any topological manifolds is an open question, as is the existence of energy functions for such flows. In this paper, we study the dynamics of regular topological flows, investigate the topology of the embedding and the asymptotic behavior of invariant manifolds of fixed points and periodic orbits. The main result is the construction of the Morse – Bott energy function for such flows, which ensures their close connection with the topology of the ambient manifold.

Ключевые слова: energy function, Morse – Bott energy function, regular topological flow, chain recurrent set, ambient manifold

Финансовая поддержка Номер гранта
Министерство образования и науки Российской Федерации 075-15-2019-1931
Российский фонд фундаментальных исследований 20-31-90069
The work on Section 3 was partially supported by the Laboratory of Dynamical Systems and Applications NRU HSE, by the Ministry of Science and Higher Education of the Russian Federation (ag. 075-15-2019-1931) and by the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS (project 19-7-1-15-1); the work on Section 4 was funded by RFBR, project number 20-31-90069.


DOI: https://doi.org/10.1134/S1560354721040031

Список литературы: PDF файл   HTML файл

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Тип публикации: Статья
MSC: 37D05, 37B20, 37B35
Поступила в редакцию: 29.03.2021
Принята в печать:23.04.2021
Язык публикации: английский

Образец цитирования: Olga V. Pochinka, Svetlana Kh. Zinina, “Construction of the Morse –Bott Energy Function for Regular Topological Flows”, Regul. Chaotic Dyn., 26:4 (2021), 350–369

Цитирование в формате AMSBIB
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\by Olga V. Pochinka, Svetlana Kh. Zinina
\paper Construction of the Morse –Bott Energy Function for Regular
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