Markov partitions for the two-dimensional torus
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- by Mark R. Snavely PDF
- Proc. Amer. Math. Soc. 113 (1991), 517-527 Request permission
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.References
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- Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283 M. R. Snavely, Markov partitions for hyperbolic automorphisms of the two-dimensional torus, Ph.D. thesis, Northwestern Univ., 1990. M. W. Stafford, Markov partitions for the doubling map, Ph.D. thesis, Northwestern Univ., 1989.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 517-527
- MSC: Primary 58F15; Secondary 28D15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1076579-0
- MathSciNet review: 1076579