Hyperbolic flows are topologically stable

Abstract

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.

Structurally stable flows

“…Also, there is a neighbourhood G C G' of / in X(M) with the property that for all g in G, there is a semiconjugacy (h, A) from g to f such that d(h, 1) < e. We claim that /i -1 ( 7 i) C U\ and hl (r, 2 )cU 2 . [10] otf(x) is the a-limit set of / at x.…”