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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2025, том 30, выпуск 2, страницы 254–278 (Mi rcd1306)

Topological Classification of Polar Flows on Four-Dimensional Manifolds

Elena Ya. Gurevich, Ilya A. Saraev

NRU HSE, ul. Bolshaya Pecherskaya 25/12, 603155 Nizhny Novgorod, Russia

Аннотация: S. Smale has shown that any closed smooth manifold admits a gradient-like flow, which is a structurally stable flow with a finite nonwandering set. Polar flows form a subclass of gradient-like flows characterized by the simplest nonwandering set for the given manifold, consisting of exactly one source, one sink, and a finite number of saddle equilibria. We describe the topology of four-dimensional closed manifolds that admit polar flows without heteroclinic intersections, as well as all classes of topological equivalence of polar flows on each manifold. In particular, we demonstrate that there exists a countable set of nonequivalent flows with a given number $k \geqslant 2$ of saddle equilibria on each manifold, which contrasts with the situation in lower-dimensional analogues.

Ключевые слова: structurally stable flows, gradient-like flows, topological classification, Kirby diagram

MSC: 37C15

Поступила в редакцию: 07.10.2024
Принята в печать: 20.02.2025

Язык публикации: английский

DOI: 10.1134/S1560354725020054



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