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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1076579-0
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.


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

  • 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, Academic Press, New York-London, 1972. Pure and Applied Mathematics, Vol. 45. 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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Article copyright: © Copyright 1991 American Mathematical Society