Criterion for the Topological Conjugacy of Multi-Dimensional Gradient-Like Flows with No Heteroclinic Intersections on a Sphere

Autor:	Vladislav E. Kruglov, Olga V. Pochinka
Rok vydání:	2020
Předmět:	Statistics and Probability Class (set theory) Pure mathematics Mathematics::Dynamical Systems Applied Mathematics General Mathematics Codimension Mathematics::Group Theory Flow (mathematics) Multi dimensional Point (geometry) Limit (mathematics) Tree (set theory) Topological conjugacy Mathematics
Zdroj:	Journal of Mathematical Sciences. 250:22-30
ISSN:	1573-8795 1072-3374
DOI:	10.1007/s10958-020-04993-w
Popis:	We study gradient-like flows with no heteroclinic intersections on an n-dimensional (n ≥ 3) sphere from the point of view of topological conjugacy. We prove that the topological conjugacy class of such a flow is completely determined by the bicolor tree corresponding to the frame of separatrices of codimension 1. We show that for such flows the notions of topological equivalence and topological conjugacy coincide (which is not the case if there are limit cycles and connections.
Databáze:	OpenAIRE
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