2006 Fiscal Year Final Research Report Summary
A study of finitary isomorphism of dynamical systems
| Project/Area Number |
17540198
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
HAMACHI Toshihiro Kyushu University, Graduate School of Mathematics, Professor emeritus, 大学院数理学研究院, 名誉教授 (20037253)
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| Co-Investigator(Kenkyū-buntansha) |
WATATANI Yasuo Kyushu University, graduate School of Mathematics, Professor, 大学院数理学研究院, 教授 (00175077)
YUASA Hisatoshi Keio University, Faculty of Science and Technology, Visiting research associate, 理工学部, 准訪問研究員 (50363346)
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| Project Period (FY) |
2005 – 2006
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| Keywords | symbolic dynamics / finitary isomorphism / Dye's theorem / embedding / orbit equivalence / Dyck shift / binary odometer / finitary orbit equivalence |
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| Research Abstract |
Finitary isomorphism has been fundamental in the study of dynamical systems. Along this line, we successfully completed our project which had to do with the embedding problem of symbolic dynamics and the finitary orbit equivalence of ergodic measure preserving transformations. In the first year we improved the embedding theorem of Krieger and Boyle, and got a new embedding theorem by which we could see how to embed a subshift of finite type by a sliding block code into the Dyck shift. This project will be going on with the collaboration with Krieger, and actually some improvements already were done with him.
In the final year, we developed the Dye theorem so that we could see the orbit equivalence map of the binary and ternary odometers in a finitary method. The advantage which this orbit equivalence map possesses is that it shows us how any digit appearing on a point of the source dynamical system (say the binary odometer) is determined by looking at only a finite block appearing on the image point by the orbit equivalence onto the target dynamical system (the ternary odometer) up to a probability zero event. Furthermore by using the idea of finitary orbit equivalence map we successfully solved the long standing problem about the certain topological orbit equivalence problem of Cantor minimal systems.
Some of these results were published on the journals (Monatshefte fur Mathematik, and Bulletin of London Math.Sci.), and also were announced at the international conferences (at Bon,2004 and at Poland,2006) and will be published on the Polish journal, Colloquium Mathematicum(2007).
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Research Products
(6 results)
