Abstract
Let M be a closed n(≥2)-dimensional smooth Riemannian manifold and let X be a vector field on M. In this paper, we show that the robust chain transitive set is hyperbolic if and only if there are a C1-neighborhood [Formula: see text] of X and a compact neighborhood U of the chain transitive set such that for any [Formula: see text], the index of the continuation on ΛY(U) = ⋂t∈ℝYt(U) of every critical point does not change.
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