2017年1月
Rotational beta expansion: ergodicity and soficness
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
- ,
- 巻
- 69
- 号
- 1
- 開始ページ
- 397
- 終了ページ
- 415
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.2969/jmsj/06910397
- 出版者・発行元
- MATH SOC JAPAN
We study a family of piecewise expanding maps on the plane, generated by composition of a rotation and an expansive similitude of expansion constant beta. We give two constants B-1 and B-2 depending only on the fundamental domain that if beta > B-1 then the expanding map has a unique absolutely continuous invariant probability measure, and if beta > B-2 then it is equivalent to 2-dimensional Lebesgue measure. Restricting to a rotation generated by q-th root of unity zeta with all parameters in Q(zeta,beta), the map gives rise to a sofic system when cos(2 pi/q) is an element of Q(beta) and beta is a Pisot number. It is also shown that the condition cos(2 pi/q) is an element of Q(beta) is necessary by giving a family of non-sofic systems for q = 5.
- リンク情報
- ID情報
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- DOI : 10.2969/jmsj/06910397
- ISSN : 0025-5645
- Web of Science ID : WOS:000393010500015