@article{oai:tsukuba.repo.nii.ac.jp:00040670,
 author = {秋山, 茂樹 and AKIYAMA, Shigeki and CAALIM, Jonathan},
 issue = {1},
 journal = {Journal of the ｍathematical society of japan},
 month = {Jan},
 note = {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), the map gives rise to a sofic system when os(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.},
 pages = {397--415},
 title = {Rotational beta expansion: ergodicity and soficness},
 volume = {69},
 year = {2017}
}