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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Markov partitions for expanding maps of the circle

Author: Matthew Stafford
Journal: Trans. Amer. Math. Soc. 324 (1991), 385-403
MSC: Primary 58F11; Secondary 58F20
MathSciNet review: 1049617
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Abstract: We study Markov partitions for orientation-preserving expanding maps of the circle whose rectangles are connected. Up to a reordering of basis elements, the class of induced matrices arising for such partitions is characterized. Then the study focuses on the subclass of partitions for which each boundary set is a periodic orbit. We show that, if the boundary orbit of a partition is well-distributed, the partition and its symmetries can be constructed. An accompanying result is concerned with double covers of the circle only. It says that, for a given period, all partitions bounded by ill-distributed orbits have the same induced matrix.

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Article copyright: © Copyright 1991 American Mathematical Society

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