# American Institute of Mathematical Sciences

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June  2009, 24(2): 613-624. doi: 10.3934/dcds.2009.24.613

## Markov partitions reflecting the geometry of $\times2$, $\times3$

 1 School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, United Kingdom 2 Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, piso 7, Santiago, Chile

Received  July 2008 Revised  November 2008 Published  March 2009

We give an explicit geometric description of the $\times2$, $\times3$ system, and use this to study a uniform family of Markov partitions related to those of Wilson and Abramov. The behaviour of these partitions is stable across expansive cones and transitions in this behaviour detect the non-expansive lines.
Citation: Thomas Ward, Yuki Yayama. Markov partitions reflecting the geometry of $\times2$, $\times3$. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 613-624. doi: 10.3934/dcds.2009.24.613
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