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Markov partitions reflecting the geometry of \(\times 2, \times 3\). (English) Zbl 1172.22004

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.

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
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