We show that a C 1 -flow on a compact Riemannian manifold is structurally stable and topologically stable if and only if it satisfies Axiom A and the strong transversality condition. This improves Smale's conjecture for flows.
We show that any hyperbolic flow (X, ir) on a metric space X is topologically stable by showing that it is expansive and has the chain-tracing property.
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