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Rotational beta expansion: ergodicity and soficness
http://hdl.handle.net/2241/00145615
http://hdl.handle.net/2241/001456153a586b2a-96da-40fa-9f43-417399efb323
名前 / ファイル | ライセンス | アクション |
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JMSJ_69-1 (4.2 MB)
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Item type | Journal Article(1) | |||||
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公開日 | 2017-03-27 | |||||
タイトル | ||||||
タイトル | Rotational beta expansion: ergodicity and soficness | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
AKIYAMA, Shigeki
× AKIYAMA, Shigeki× CAALIM, Jonathan |
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著者別名 |
秋山, 茂樹
× 秋山, 茂樹 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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. | |||||
書誌情報 |
Journal of the mathematical society of japan 巻 69, 号 1, p. 397-415, 発行日 2017-01 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0025-5645 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0070177X | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.2969/jmsj/06910397 | |||||
権利 | ||||||
権利情報 | © 2017 The Mathematical Society of Japan | |||||
著者版フラグ | ||||||
値 | publisher | |||||
出版者 | ||||||
出版者 | The Mathematical Society of Japan |