2015/02/06 by Shigeki Akiyama, Akiyama, Shigeki, Jonathan Caalim +1
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Theoretical and Computational Physics #math.DS #math.NT
paper · pdf · doi:10.48550/arxiv.1502.01793
Revised version: to appear in JMSJ after certain edition
openalex publication_date 2015/02/06 · arxiv created 2015/09/15 · arxiv updated 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a family of piecewise expanding maps on the plane, generated by composition of a rotation and an expansive similitude of expansion constant β. We give two constants B1 and B2 depending only on the fundamental domain that if β>B1 then the expanding map has a unique absolutely continuous invariant probability measure, and if β>B2 then it is equivalent to 2-dimensional Lebesgue measure. Restricting to a rotation generated by q-th root of unity ζ with all parameters in ℚ(ζ,β), it gives a sofic system when cos(2π/q) ∈ ℚ(β) and β is a Pisot number. It is also shown that the condition cos(2π/q) ∈ ℚ(β) is necessary by giving a family of non-sofic systems for q=5.