Attractors with irrational rotation number
2011 ◽
Vol 153
(1)
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pp. 59-77
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Keyword(s):
AbstractLet h: 2 → 2 be a dissipative and orientation preserving homeomorphism having an asymptotically stable fixed point. Let U be the region of attraction and assume that it is proper and unbounded. Using Carathéodory's prime ends theory one can associate a rotation number, ρ, to h|U. We prove that any map in the above conditions and with ρ ∉ induces a Denjoy homeomorphism in the circle of prime ends. We also present some explicit examples of maps in this class and we show that, if the infinity point is accessible by an arc in U, ρ ∉ if and only if Per(h) = Fix(h) = {p}.
2014 ◽
Vol 24
(01)
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pp. 1450012
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1985 ◽
Vol 5
(1)
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pp. 27-46
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Keyword(s):
2005 ◽
Vol 15
(11)
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pp. 3675-3689
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2012 ◽
Vol 274
(1-2)
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pp. 315-321
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2021 ◽
pp. 287-300
2013 ◽
Vol 13
(1)
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pp. 19-41
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Keyword(s):
2011 ◽
Vol 140
(1)
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pp. 227-233
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Keyword(s):