Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1991-1049617-3
MathSciNet review: 1049617
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F11, 58F20

Retrieve articles in all journals with MSC: 58F11, 58F20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1049617-3
Article copyright: © Copyright 1991 American Mathematical Society