Clarification on topological models for ergodic transformation groups having infinite invariant measures
| Project/Area Number |
15K04900
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka Kyoiku University |
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Principal Investigator |
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| Research Collaborator |
Hama Masaki
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 保測変換 / 無限ルベーグ空間 / 狭義エルゴード性 / 代入 / S-進性 / エルゴード性 / 無限保測変換 / 位相的実現 / 非原始的代入 / 線形再帰性 / ブラッテリ-ヴェルシック表現 / 無限不変測度 / 因子写像 / 位相モデル / 一意エルゴード的 / 局所コンパクトカントル極小系 |
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| Outline of Final Research Achievements |
I could prove the following three facts. Any factor map between ergodic measure-preserving transformations on infinite Lebesgue spaces is realized up to a measure theoretical isomorphism as a topological semi-conjugacy between strictly ergodic, locally compact Cantor systems. In the category of ergodic measure-preserving systems on infinite Lebesgue spaces, any diagram without any extension of two common transformations is realized up to a measure theoretical isomorphism as that of strictly ergodic, locally compact Cantor systems. The S-adic property is possessed by Bratteli-Vershik representations associated with almost minimal subshifts arising from non-primitive substitutions with a certain property between the maximal and second maximal eigenvalues of their incidence matrices.
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| Academic Significance and Societal Importance of the Research Achievements |
狭義エルゴード的同型表現定理は，分野の歴史と照らし合わせると，大変に重要である．事実，確率保測エルゴード変換に対する同型表現定理はW.Kriegerによって一般的な形で解決され，エルゴード理論の教科書にはよく掲載されている．一方で，殆ど原始的代入に付随する殆ど極小サブシフトのS-進性については，全く未開の領域であり，さらには非定常性を呈することが解明できたことは，原始的代入に付随するサブシフトにはなかった新しい現象である．
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Report
(5 results)
Research Products
(9 results)
