Genericity for non-wandering surface flows

Tomoo Yokoyama

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arXiv · 1301.0407

Genericity for non-wandering surface flows

Tomoo Yokoyama

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Abstract

Consider the set $\chi^0_{\mathrm{nw}}$ of non-wandering continuous flows on a closed surface. Then such a flow can be approximated by regular non-wandering flows without heteroclinic connections nor locally dense orbits in $\chi^0_{\mathrm{nw}}$. Using this approximation, we show that a non-wandering continuous flow on a closed connected surface is topologically stable if and only if the orbit space of it is homeomorphic to a closed interval. Moreover we state the non-existence of topologically stable non-wandering flows on closed surfaces which are not neither $\mathbb{S}^2$, $\mathbb{P}^2$, nor $\mathbb{K}^2$.

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Tomoo Yokoyama. 2013-01-03. Genericity for non-wandering surface flows. https://arxiv.org/abs/1301.0407

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