Ward, Thomas B.; Yayama, Yuki Markov partitions reflecting the geometry of \(\times 2, \times 3\). (English) Zbl 1172.22004 Discrete Contin. Dyn. Syst. 24, No. 2, 613-624 (2009). The purpose of this paper is to study geometrically natural Markov partitions like those used by Abramov and Wilson for an example in which Archimedean directions arise in tangent space. The authors study how the structure of those partitions changes in expansive cones. In order to do this, they describe the structure of the space obtained by taking the invertible extension of the \(\mathbb{N}^2\)-action generated by the maps \(x\to 2x\pmod 1\) and \(x\to 3x\pmod 1\) on the additive circle in a geometric way. Reviewer: Ulrich Krengel (Göttingen) Cited in 1 Document MSC: 37A15 General groups of measure-preserving transformations and dynamical systems 22D40 Ergodic theory on groups 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory Keywords:Markov partition; expansive subdynamics; solenoid PDFBibTeX XMLCite \textit{T. B. Ward} and \textit{Y. Yayama}, Discrete Contin. Dyn. Syst. 24, No. 2, 613--624 (2009; Zbl 1172.22004) Full Text: DOI arXiv