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2015 Fiscal Year Final Research Report

Pisot conjecture on substitutive dynamical systems

Research Project

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Project/Area Number 24540012
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionUniversity of Tsukuba

Principal Investigator

Akiyama Shigeki  筑波大学, 数理物質系, 教授 (60212445)

Co-Investigator(Kenkyū-buntansha) KOMATSU Kazushi  高知大学, 理学部, 准教授 (00253336)
Project Period (FY) 2012-04-01 – 2016-03-31
Keywordsピゾ数 / 置換規則 / 自己誘導構造 / タイリング / 自然拡大 / 概周期構造 / 準結晶
Outline of Final Research Achievements

Substitutive dynamical system models self-inducing structure appears in general dynamical systems. It is generated by a substitution rule on finite letters. Such system realized as self-similar tiling can not be strongly mixing and whether it is weakly mixing or not is described by whether the dilation is a Pisot number.
We studied the well-known conjecture in this area which asserts that every irreducible Pisot substituion is pure discrete. As a result with J.Y.Lee we elucidated relationship between several coincidence conditions. Further with J.Y.Lee and F.Gahler, we did a systematic valification of the conjecture up to trace 2. All of them are pure discrete, we did not find a counter example.

Free Research Field

数論

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Published: 2017-05-10  

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