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Pointwise chain recurrent maps of the space Y
Published online by Cambridge University Press: 17 April 2009
Abstract
Let Y = {z ∈ C: z3 ∈ [0, 1]} (equipped with subspace topology of the complex space C) and let f: Y → Y be a continuous map. We show that if f is pointwise chain recurrent (that is, every point of Y is chain recurrent under f), then either f12 is the identity map or f12 is turbulent. This result is a generalisation to Y of a result of Block and Coven for pointwise chain recurrent maps of the interval.
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- Copyright © Australian Mathematical Society 2003
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