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Generating special Markov partitions for hyperbolic toral automorphisms using fractals

Published online by Cambridge University Press:  19 September 2008

Tim Bedford
Tim Bedford
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16, Mill Lane, Cambridge, England
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Abstract

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We show that given some natural conditions on a 3 × 3 hyperbolic matrix of integers A(det A = 1) there exists a Markov partition for the induced map A(x + ℤ3) = A(x)+ℤ3 on T3 whose transition matrix is (A−1)t. For expanding endomorphisms of T2 we construct a Markov partition so that there is a semiconjugacy from a full (one-sided) shift.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 3 , September 1986 , pp. 325 - 333
Copyright
Copyright © Cambridge University Press 1986

References

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