A certain finiteness property of Pisot number systems

DOI10.1016/j.jnt.2004.02.001zbMath1052.11055OpenAlexW2018793453MaRDI QIDQ1827524

Hui Rao, Shigeki Akiyama, Wolfgang Steiner

Publication date: 6 August 2004

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.02.001

zbMATH Keywords

Pisot numberbeta expansionweak finiteness

Mathematics Subject Classification ID

Radix representation; digital problems (11A63) Symbolic dynamics (37B10) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06)

Related Items

Purely periodic 𝛽-expansions with Pisot unit base, Dynamical directions in numeration, Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to \(\beta\)-shifts, Atomic surfaces, tilings and coincidences. II: Reducible case, Spectral properties of cubic complex Pisot units, On alpha-adic expansions in Pisot bases, On the distribution of certain Pisot numbers, Beta-expansions, natural extensions and multiple tilings associated with Pisot units, The Pisot conjecture for -substitutions, Symmetrized \(\beta \)-integers, Tilings for Pisot beta numeration, Digit frequencies and Bernoulli convolutions, Atomic surfaces, tilings and coincidence. I: Irreducible case, Beta-expansions of -adic numbers, Substitutive number systems, On numbers having finite beta-expansions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ergodic-theoretic properties of certain Bernoulli convolutions
• On the boundary of self-affine tilings generated by Pisot numbers
• Bijective and general arithmetic codings for Pisot toral automorphisms
• On the characterization of canonical number systems
• Markov subshifts and realization of \(\beta\)-expansions
• Finite beta-expansions
• Nombres algébriques et substitutions
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• New criteria for canonical number systems
• Pisot substitutions and Rauzy fractals