
A new definition of separatrix is introduced and the theory developed is applied to the study of the topological structure of singular points. Each component of the complement of the separatrix set in a neighborhood of an isolated singular point is shown to satisfy one of seven types of behavior.
510.mathematics, Dynamical systems and ergodic theory, Ordinary differential equations and systems on manifolds, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, flow on an n-dimensional manifold, topological structure of singular points, Article
510.mathematics, Dynamical systems and ergodic theory, Ordinary differential equations and systems on manifolds, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, flow on an n-dimensional manifold, topological structure of singular points, Article
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