Vector fields with a given set of singular points

DOI10.1007/BF02487440zbMATH Open0933.57024arXivmath/9901116OpenAlexW2067440649MaRDI QIDQ4941417

Alexander Prishlyak

Publication date: 8 March 2000

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Abstract: Theorems on the existence of vector fields with given sets of Indexes of isolated Singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a two-dimensional manifold, an index of an isolated Singular point of the gradient field is not greater than one.

Full work available at URL: https://arxiv.org/abs/math/9901116

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

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