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Research of complex dynamical systems and C*-algebras

Research Project

Project/Area Number 23540242
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionOkayama University

Principal Investigator

Kajiwara Tsuyoshi  岡山大学, その他の研究科, 教授 (50169447)

Co-Investigator(Renkei-kenkyūsha) WATATANI Yasuo  九州大学, 大学院数理学研究院, 教授 (00175077)
Project Period (FY) 2011-04-28 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsC*-環 / 複素力学系 / 自己相似写像 / 双加群 / トレース / イデアル / KMS 状態 / C*環 / ヒルベルト双加群 / K-群 / 有理関数 / コア / 軌道同型 / 分岐点 / KMS state / C* 環 / 次元群
Outline of Final Research Achievements

We showed that graph C*-algebras have finite type KMS stated associated with sinks of the graphs. We showed that we can recover the information of the backward orbits of branched points from KMS states of the C*-algebras associated with the dynamics of rational functions on the Riemannian sphere.
We classified finite traces on the cores of the C*-algebras associated with self-similar maps under a technical assumption for branched points. Moreover, we described the matrix representation of the finite cores of the C*-algebras associated with self-similar maps, and using the matrix representation, we classified ideals of the core of the C*-algebras associated with self-similar maps under the same assumption.

Report

(6 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (17 results)

All 2016 2015 2014 2013 2012 2011 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 2 results) Presentation (9 results) Remarks (3 results)

  • [Journal Article] Ideals of the cores of the C*-algebras constructed from self-similar maps2016

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Journal of Operator Theory

      Volume: 75 Pages: 1225-1255

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Traces on cores of C*-algebras associated with self-similar maps2014

    • Author(s)
      Tsuyoshi Kajiwara and Yasuo Watatani
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: 34 Issue: 6 Pages: 1964-1989

    • DOI

      10.1017/etds.2013.26

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] C*-algebras associated with complex dynamical systems and backward orbit structure2014

    • Author(s)
      Tsuyoshi Kajiwara and Yasuo Watatani
    • Journal Title

      Complex analysis and Operator Theory

      Volume: 6 Pages: 243-254

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] KMS states of finite-graph algebras2013

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 67 Pages: 83-104

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] C*-algebras associated with complex dynamical systems and backward orbit structure2013

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Complex Analysis and Operator Theory

      Volume: Online Issue: 1 Pages: 243-254

    • DOI

      10.1007/s11785-013-0293-7

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 2次元自己相似写像に付随するC*-環の解析2016

    • Author(s)
      梶原 毅、綿谷安男
    • Organizer
      日本数学会年会
    • Place of Presentation
      茨城県 筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 非可逆力学系から作られる C*-環のコアの解析2015

    • Author(s)
      梶原 毅、綿谷安男
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京都明治大学
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] 複素力学系から作られる C*-環の極大可換環と連続軌道同型2014

    • Author(s)
      綿谷安男、梶原毅
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島県広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 自己相似写像から作られるC*-環のコアの行列表示とK-群2014

    • Author(s)
      梶原 毅、綿谷安男
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 複素力学系から作られるC*-環のコアの離散トレース2013

    • Author(s)
      梶原 毅、綿谷安男
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 複素力学系から作れるC*-環のコアのトレース2013

    • Author(s)
      梶原 毅, 綿谷安男
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都府京都市京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 自己相似写像から作られるC*-環のコアのイデアル2012

    • Author(s)
      梶原 毅, 綿谷安男
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      福岡県福岡市九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 自己相似写像から作られる C*環のコアの行列表示2012

    • Author(s)
      梶原 毅、綿谷安男
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京都東京理科大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 自己相似写像から作られる C*環のコアの解析2011

    • Author(s)
      梶原 毅、綿谷安男
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      長野県松本市信州大学
    • Related Report
      2011 Research-status Report
  • [Remarks]

    • URL

      http://www.ems.okayama-u.ac.jp/ems_2/kajiwara/homeJapan.html

    • Related Report
      2015 Annual Research Report
  • [Remarks]

    • URL

      http://www.ems.okayama-u.ac.jp/ems_2/kajiwara/homeJapan.html

    • Related Report
      2014 Research-status Report
  • [Remarks] 岡山大学環境理工学部環境数理学科

    • URL

      http://www.ems.okayama-u.ac.jp/ems_2/kajiwara/homeJapan.html

    • Related Report
      2013 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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