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Stability of parametrized families of gradient vector fields. (English) Zbl 0533.58018
This paper studies the structural stability of a $$C^{\infty}$$ one parameter family of gradient vector fields defined on a closed $$C^{\infty}$$ manifold. Let $$X^ g\!_ 1(M)$$ be the set of such vector fields endowed with the $$C^{\infty}$$ Whitney topology. The main result of the paper is the following. Theorem. There exists an open and dense G C $$X^ g\!_ 1(M)$$ such that if $$\{X_{\mu}\}$$ is in G then $$\{\chi_{\mu}\}$$ is structurally stable.
Reviewer: M.Teixeira

##### MSC:
 37C75 Stability theory for smooth dynamical systems 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 57R25 Vector fields, frame fields in differential topology
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