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Research on ergodic theory and its applications

Research Project

Project/Area Number 06452017
Research Category

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

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

Principal Investigator

ITO Yuji  Keio Univ., Math.Dep't Professor, 理工学部, 教授 (90112987)

Co-Investigator(Kenkyū-buntansha) SHIOKAWA Iekata  Keio Univ., Math.Professor, 理工学部, 教授 (00015835)
MAEDA Yoshiaki  Keio Univ., Math.Professor, 理工学部, 教授 (40101076)
ENOMOTO Hikoe  Keio Univ., Math.Professor, 理工学部, 教授 (00011669)
TANAKA Hiroshi  Keio Univ., Math.Professor, 理工学部, 教授 (70011468)
NAKADA Hitoshi  Keio Univ., Math.Assoc.Prof., 理工学部, 助教授 (40118980)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 1995: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1994: ¥3,900,000 (Direct Cost: ¥3,900,000)
Keywordstype II^* & III transformations / Radon-Nikodym cocycles / exhaustive weakly wandering sequences / direct sum decompostion of 2 / multiple recurrence / Kakutani-Parry index / cutting and stacking method / complexity of sequences / II_∞型及びIII型エルゴード変換 / ラドン・ニコディム・コサイクル / exhaustive weakly wandering seq. / 多重再帰性 / cutting and stacking構成法 / 符号列のComplexity / II_∞型エルゴード変換 / Zの直和分解 / Gauss数体上の連分数近似 / 3次元ビリヤードの符号列 / 量子的エルゴード性 / ブラウン媒質内の拡散過程 / 自己相似過程 / 局所誘導方程式
Research Abstract

In this project, researches concerning diversified areas connected with ergodic theory were carried out by a number of mathematicians working in the areas of ergodic theory, probability theory, functional analysis, analytic number theory, combinatorics and differential geometry, and many significant results were obtained.
1. In ergodic theory proper, properties of ergodic transformations which are characteristic for transformations having no finite invariant measures (so-called typ II_* and type III transformations) were investigated in depth. In particular, asymptotic behavior of the Radon-Nikodym cocycles and properties of exhaustive weakly wandering sequences and their relation to the direct sum decomposition of the integers Z were studied and a number of interesting results were obtained. Furthermore, multiple recurrence properties of type II_* transformations were studied and their relation with Kakutani-Parry index was established.
2. Concerning the interrelation between ergodic theory and othe areas, complexity of th esymbolic sequences associated with 3-dimensional billiard was determined, and sharp L^*-norm estimates for eigen functions for Laplacian on hyperbolic 3 manifolds were obtained.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (41 results)

All Other

All Publications (41 results)

  • [Publications] Yuji Ito,: "Cocycles for non-singular transformations" Commentarii Math. Univ. Sancti Panti. 44. 93-103 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Yuji Ito: "Direct sum decomposition of the integers" Tokyo Journal of Mathematics. 18. 259-270 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hitoshi Nakada: "Dynamics of complex continued fractions and geodesics over H^3" The Proceedings of International Conference of Dynamical Systems and Ohaos. 192-199 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Kozono,Y.Maeda,H.Naito: "Global solutions for the Yang-Mills Gradient flow on 4-manifolds" Nagoya Mathematical Journal. 139. 93-128 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Enomoto: "Graph decompositions without isolated vertices" Jour. of Combinatorial Theory (Ser. B). 63. 111-124 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Shinya Koyama: "L^∞-norms of eigenfunctions for hyperbolic three manifolds" Duke Math. Journal. 77. 799-817 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Yuji Ito & M.Yoshida: "Cocycles for non-singular transformtions" Commentarii Math.Univ.St.Pauli. 44. 93-103 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Yuji Ito: "Direct sum decomposition of the integers" Tokyo Jour.of Math. 18. 259-270 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hitoshi Nakada: "Dynamics of complex continued fractions and geodesics over H^3" The Proc.of International Conf.of Dynamical Systems and Chaos. 192-199 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Kozono, Y.Maeda & H.Naito: "Clobal solutions for the Yang-Mills gradient flow on 4-manifolds" Nagoya Math.Jour. 139. 93-128 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Enomoto: "Graph decompositions without isolated vertices" Jour.of Combinatorial Theory (Ser.B). 63. 111-124 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Koyama: "H^*-norms of eigenfunctions for hyperbolic three manifolds" Duke Math.Jour. 77. 799-817 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Yuji Ito, Masamichi Yoshida: "Cocycles for non-singular transformations" Commentarii Math. Univ. Sarcti Pauli. 44. 93-103 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Yuji Ito: "Direct sum decomposition of the integers" Tokyo Journal of Math.18. 259-270 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hitoshi Nakada: "Dynamics of Complex continued fractions and geodesics over H^3" The Proceedings of International Conference of Dynamical Systems and Chaos. 192-199 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] H. Kozono, Y. Maeda, H. Naito: "Global solutions for the Yang-Mills gradient flow on 4-manifolds" Nagoya Mathematical Journal. 139. 93-128 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] H. Enomoto: "Graph decompostions without isolated vertices" Jour. of Combinatorial Theory (Ser. B). 63. 111-124 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Shinya Koyama: "L^∞ norms of eigenfunctions for hyperbolic three manifolds" Duke Math. Journal. 77. 799-817 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Ito,Y.: "Direct sum decomposition of the integers" Tokyo Journal of Mathematics. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Ito,Y.& Yoshida,M.: "Cocycles for non-singular transformations" Comment.Math.Univ.St.Pauli. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Nakada,H.: "Continued fractions,geodesic flows and Ford circles" Algorithms,Fractals and Dynamics. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Tanaka,H.: "Localization of a diffusion process in a one-dimensional Brounian environment" Commun.Pure Appl.Math.47. 755-766 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tanaka,H.: "Diffusion processes in random environ ments" Proceedings of ICM94. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Maejima,M.& Mason,D.: "Operator-self-similar stable processes." Stochastic Processes & their Applications. 54. 139-163 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Maejima,M.: "Operator-stable processes and operator fractional stable motions" Probability and Mathematical Statistics. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Maejima,M.& Rachev,S.T.: "Rate of convergence in the operator-stable limit theorem" Journal of Theoretical Probability. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Omori,H.,Maeda,Y.& Yoshioka,A.: "Deformation quantization of Poisson algebras" Contemporary of Mathematics. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Kawazoe,T.,Onoe,Y.& Tachizawa,K.: "Functions on the real line with nonnegative Fouriertransforms" Tohoku Matb.Journal. 46. 311-320 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Kawazoe,T.: "Functions on noncompact Lie groups with positive Fourier transforms" Proceedings of Amer.Math.Soe.(to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Tani,A.,Itoh,S.& Tanaka,N.: "The initial value problem for the in compressible Navierstokes equations with general slip boundary condition" Adv.Math.Sci.Appl.4. 51-69 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Nishiyama,T.& Tani,A.: "Solvability of the localized induction eqnation for vortex motion" Comm.Math.Phys.16. 433-445 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Tani,A.& Tanaka,N.: "Large time existence of Surface waves in incompressible viscous fluids with or without surface tension" Arch.Rat.Mech.Anal.(to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Tani,A.: "Small-time existence for the three-dimensional in compressible Navier-Stokes equations with a free surface" Arch.Rat.Mech.Anal.(to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Arai,T.& Ishikawa,S.& Kawai,T.: "Numerical Analysis of trajectories of a quantum particle in two-slit experiment" International Jour.of Theoretical Pbysics. 33. 1265-1274 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Arnoux,P.Manduit,C.Shiokawa,I,& Tamura,J.: "Complexity of sequences defined by billiard in the cube" Bull.Soc.Math.France. 122. 1-12 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Arnoux,P.,Manduit,C.Shiokawa,I.& Tamura,J: "Rauzy's conjecture on billiards in the cube" Tokyo Jour.of Mathematics. 17. 211-218 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Enomoto,H.& Kaneko,A.: "The condition of Beineke and Harary.on edge-disjoint paths some of which are openly disjoint" Tokyo,Journal of Mathematics. 17. 355-357 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Enomoto,H.: "Graph decompositions without isolated vertices" Jour.of Combinatorial Theory. 63. 111-124 (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] Enomoto,H.& Kano,M.: "Disjoint odd integer subsets having a constant even sum" Discrete Math.137. 189-193 (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] Enomoto,H.,van den Heuvel Kaneko,A.& Saito.A.: "Relative length of long paths and cycles in graphs with large degree sums" Journal of Graph Theory. (to appear in).

    • Related Report
      1994 Annual Research Report
  • [Publications] Koyama,S.: "L^∞norms of eigenfunctions for hyperbolic three spaees" Duke Mathematical Journal. (1994)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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