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1994 Fiscal Year Final Research Report Summary

Theoretical Study of Chaotic Phenomena

Research Project

Project/Area Number 05452015
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTokyo Metropolitan University

Principal Investigator

AOKI Nobuo  Tokyo Metropolitan Univ.Faculty of Science, Professor, 理学部, 教授 (60087020)

Co-Investigator(Kenkyū-buntansha) 平田 雅樹  東京都立大学, 理学部, 助手 (70254141)
MATSUI T  Faculty of Science, Professor, 理学部, 助教授 (50199733)
NISHIOKA K  Faculty of Science, Professor, 理学部, 助教授 (60101078)
YAMASHITA S  Faculty of Science, Professor, 理学部, 助教授 (30087019)
TOMIYAMA J  Faculty of Science, Professor, 理学部, 教授 (30006928)
HIRATA M  Faculty of Science, Assistant Professor
Project Period (FY) 1993 – 1994
Keywordschaos / sensitive / manifold / dynamical system / prediction / 現象
Research Abstract

Lorenz in his remarble work on the dynamical modelling of weather prediction stressed implying that some degree of uncertainty of such a prediction is unavoidable and no matter how accurate are the initial data.
On the work of Lorenz it can be seen that chaotic behavior of a system with respect to initial condition was introduced in the area of dynamical systems theory. Usually, a dynamical system is given as a transformation on a space of events. This space of events can be a manifold.
Concerning dynamical systems on a manifold, an interesting problem is posed as follows :
"Are the diffeomorphisms with axiom A C^1-dense in the space of all surface diffeomorphisms? "
Our project could give an answer for this important problem.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] Nobuo Aoki: "The set of axiom A diffeomorphisms with no cycles" Bol.Soc.Bras.Math.23. 21-65 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Aoki,J.Tomiyama: "Characterizations of topological dynamical systems…" Ergod.Th.& Dynami.Sys.13. 1-5 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Shinji Yamashita: "The Poincare′ density,Lipschiz continuity" Math.Japonica. 38. 487-496 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Taku Matui: "Markov semigroups on UHF algebras21GC04:Reviews in Math.Physcis" 5. 587-600 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Taku Matsui: "On conservation laws of the XY model" H.Araki(eds.)Quantum and Non‐Commutative Analysis. 197-204 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Taku Matsui: "Markov Semigroups which dcscribe the time evolution" J.Fun.Anal.116. 179-198 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Aoki,K.Hiraide: "Topological Theory of Dynamical Systems" Elsevier,North Holand, 400 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Nobuo Aoki: "The set of axiom A diffeomorphisms with no cycles" Bol.Soc.Bras.Math.Vol.23. 21-65 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Aoki, J.Tomiyama: "Characterizations of topological systems..." Ergod.Th.& Dynami.Sys.Vol.13. 1-5 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Shinji Yamashita: "The Poincare'density, Lipshitz continuity" Math.Japonica. Vol.38. 487-496 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Taku Matsui: "Markov semigroups on UHF algebras" Reviews in Math.Phisics. Vol.5. 587-600 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Taku Matsui: "On conservation laws of the XY model" H.Araki (eds.) Quantum and Non-commutative Analysis. 197-204 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Taku Matsui: "Markov Semigroups which describe the time evolution" J.Fun.Anal. Vol.116. 179-198 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Aoki, K.Hiraide: Topological Theory of Dynamical Systems. Elsevier, North Holand, 400 (1994)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1996-04-15  

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