Generating special Markov partitions for hyperbolic toral automorphisms using fractals
Open Access
- 1 June 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 6 (3) , 325-333
- https://doi.org/10.1017/s0143385700003527
Abstract
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.Keywords
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