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Lyapunov stability of $\omega$-limit sets

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  • We prove that there is a residual subset $C$, in the space of all $\mathcal C^1$ vector fields of a closed $n$-manifold $M$, such that for every $X \in \mathcal R$ the set of points in $M$ with Lyapunov stable $\omega$-limit set is residual in $M$. This improves a result in Arnaud [1] and gives a partial solution to a conjecture in Hurley [8].
    Mathematics Subject Classification: Primary: 37Dxx, 37Bxx, 34Bxx.

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