Markov partitions for expanding maps of the circle

Stafford, Matthew

doi:10.1090/S0002-9947-1991-1049617-3

Markov partitions for expanding maps of the circle
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by Matthew Stafford

Trans. Amer. Math. Soc. 324 (1991), 385-403

DOI: https://doi.org/10.1090/S0002-9947-1991-1049617-3

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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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Markov partitions for the doubling map