| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| 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.
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