Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions

2007/10/18 by Shigeki Akiyama, S. Akiyama, G. Barat +9
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #math.DS #math.NT #msc:03D45 #msc:11A63 #msc:11S99 #msc:28A75 #msc:52C23 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0710.3584

arxiv created 2007/10/18 · arxiv updated 2009/12/01

Abstract

This paper studies tilings related to the beta-transformation when beta is a Pisot number (that is not supposed to be a unit). Then it applies the obtained results to study the set of rational numbers having a purely periodic beta-expansion. Special focus is given to some quadratic examples.

Related

• Tilings for Pisot beta numeration
• Purely periodic beta-expansions in the Pisot non-unit case
• Beta Expansions for Regular Pisot Numbers
• Multiple tilings associated to d-Bonacci beta-expansions
• Purely periodic expansions in systems with negative base