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

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

Thomas Ward 1, and  Yuki Yayama 2,

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.
Keywords: Markov partition, solenoid., expansive subdynamics.
Mathematics Subject Classification: Primary: 22D40, 37A15; Secondary: 37A3.
Citation: Thomas Ward, Yuki Yayama. Markov partitions reflecting the geometry of $\times2$, $\times3$. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 613-624. doi: 10.3934/dcds.2009.24.613
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