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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Markov partitions for the two-dimensional torus

Author: Mark R. Snavely
Journal: Proc. Amer. Math. Soc. 113 (1991), 517-527
MSC: Primary 58F15; Secondary 28D15
MathSciNet review: 1076579
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Abstract: We examine Markov partitions for hyperbolic automorphisms of $ {\mathbb{T}^2}$ in the spirit of Adler, Weiss, and others and give necessary conditions on the transition matrix of a Markov partition for a given automorphism. We give necessary and sufficient conditions for partitions with two connected rectangles.

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PII: S 0002-9939(1991)1076579-0
Article copyright: © Copyright 1991 American Mathematical Society