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A weakly mixing tiling dynamical system with a smooth model

✍ Scribed by Thomas L. Fitzkee; Kevin G. Hockett; E.Arthur Robinson Jr.

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 306 KB
Volume: 303
Category: Article
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(02)00501-7

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✦ Synopsis

We describe a weakly mixing one-dimensional tiling dynamical system in which the tiling space is modeled by a surface M of genus 2. The tiling system satisÿes an in ation, and the in ation map is modeled by a pseudo-Anosov di eomorphism D on M . The expansion coe cient Â for D is a non-Pisot number. In particular, the leaves of the expanding foliation for D are tiled by their visits to the elements of a Markov partition for D. The tiling dynamical system is an almost 1:1 extension of the unit speed ow along these leaves.

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