Some compact invariant sets for hyperbolic linear automorphisms of torii
1988 ◽
Vol 8
(2)
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pp. 191-204
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Keyword(s):
AbstractIf the action induced by a pseudo-Anosov map on the first homology group is hyperbolic, it is possible, by a theorem of Franks, to find a compact invariant set for the toral automorphism associated with this action. If the stable and unstable foliations of the Pseudo-Anosov map are orientable, we show that the invariant set is a finite union of topological 2-discs. Using some ideas of Urbański, it is possible to prove that the lower capacity of the associated compact invariant set is >2; in particular, the invariant set is fractal. When the dilatation coefficient is a Pisot number, we can compute the Hausdorff dimension of the compact invariant set.
1999 ◽
Vol 19
(2)
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pp. 523-534
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2005 ◽
Vol 15
(11)
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pp. 3589-3594
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1997 ◽
Vol 17
(1)
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pp. 147-167
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2009 ◽
Vol 29
(1)
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pp. 281-315
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1997 ◽
Vol 3
(18)
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pp. 114-118
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1991 ◽
Vol 01
(03)
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pp. 667-679
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2012 ◽
Vol 22
(08)
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pp. 1250195
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Keyword(s):
1996 ◽
Vol 48
(1)
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pp. 125-133
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2017 ◽
Vol 53
(13)
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pp. 1715-1733
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Keyword(s):