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Topological stability: Some fundamental properties. (English) Zbl 0545.34035

The purpose of this paper is to clarify and generalize some properties and results related to topological stability which are stated in the literature. The question whether the stability property of one parameter flow is invariant under conjugacy is answered here. What is presented is also a unified proof for showing that the pseudo orbit tracing property is a necessary condition for stability. Also there are some results related to specification property and abstract \(\omega\)-limit sets.

MSC:

34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
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