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Attractors with irrational rotation number
Published online by Cambridge University Press: 12 December 2011
Abstract
Let 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}.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 1 , July 2012 , pp. 59 - 77
- Copyright
- Copyright © Cambridge Philosophical Society 2011
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