Proper minimal sets on compact connected 2-manifolds are nowhere dense
2008 ◽
Vol 28
(3)
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pp. 863-876
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Keyword(s):
AbstractLet $\mathcal {M}^2$ be a compact connected two-dimensional manifold, with or without boundary, and let $f:{\mathcal {M}}^2\to \mathcal {M}^2$ be a continuous map. We prove that if $M \subseteq \mathcal {M}^2$ is a minimal set of the dynamical system $(\mathcal {M}^2,f)$ then either $M = \mathcal {M}^2$ or M is a nowhere dense subset of $\mathcal {M}^2$. Moreover, we add a shorter proof of the recent result of Blokh, Oversteegen and Tymchatyn, that in the former case $\mathcal {M}^2$ is a torus or a Klein bottle.
2007 ◽
Vol 5
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pp. 195-200
2018 ◽
Vol 28
(04)
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pp. 1830011
2003 ◽
Vol 13
(07)
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pp. 1721-1725
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Keyword(s):
Keyword(s):
2000 ◽
Vol 128
(10)
◽
pp. 3047-3057
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Keyword(s):