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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
  • Roy L. Adler and Benjamin Weiss, Similarity of automorphisms of the torus, Memoirs of the American Mathematical Society, No. 98, American Mathematical Society, Providence, R.I., 1970. MR 0257315
  • Robert L. Devaney, An introduction to chaotic dynamical systems, The Benjamin/Cummings Publishing Co., Inc., Menlo Park, CA, 1986. MR 811850
  • K. H. Kim and F. W. Roush, Some results on decidability of shift equivalence, J. Combin. Inform. System Sci. 4 (1979), no. 2, 123–146. MR 564188
  • 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.
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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