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

Thomas Ward; Yuki Yayama

doi:10.3934/dcds.2009.24.613

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2009, Volume 24, Issue 2: 613-624. Doi: 10.3934/dcds.2009.24.613

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

Thomas Ward^1, and
Yuki Yayama²

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

Received: June 30, 2008

Revised: October 31, 2008

Published: May 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 22D40, 37A15; Secondary: 37A35.

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