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Research of a boundary of a Coxeter system and dimension theory

Research Project

Project/Area Number 16540067
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionShimane University

Principal Investigator

YOKOI Katsuya  Shimane University, Mathematics, Associate Professor, 総合理工学部, 助教授 (90240184)

Co-Investigator(Kenkyū-buntansha) HOSAKA Tetsuya  Utsunomiya University, Mathematics, Associate Professor, 教育学部, 助教授 (50344908)
KIMURA Makoto  Shimane University, Mathematics, Professor, 総合理工学部, 教授 (30186332)
HATTORI Yasunao  Shimane University, Mathematics, Professor, 総合理工学部, 教授 (20144553)
FURUMOCHI Tetsuo  Shimane University, Mathematics, Professor, 総合理工学部, 教授 (40039128)
MAEDA Sadahiro  Shimane University, Mathematics, Professor, 総合理工学部, 教授 (40181581)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordstransitive / graph / Coxeter group / compactness degree / コンパクト指数 / コクセター / コクセター系 / 区分的単調写像 / 次元関数
Research Abstract

We studied :
(K.Yokoi)
1. the relation between transitivity and strong transitivity for graph self-maps,
2. a Barge-Martin type theorem for graph self-maps for which the set of periodic points is dense,
(T.Hosaka)
3. the interior of the limit set of a group acting on a hyperbolic or CAT(0) space,
4. dense subsets of the boundary of a Coxeter groups,
5. Coxeter systems with two-dimensional Davis-Vinberg complexes,
6. strong rigidity and strong reflection rigidity of Coxeter systems of dihedral gropus,
7. boundaries of parabolic subgroups of Coxeter groups,
8. the minimality of the boundary of a Coxeter systems,
9. reflection groups of geodesic spaces,
(M.Kimura)
10. congruent classes of Frenet curves of order 2 in the complex quadric,
11. the possibility of different presentations of spaces as unions or partitions of locally compact subspaces, and
(Y.Hattori)
12. there is no upper bound of small transfinte compactness degree in metrizable spaces.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (50 results)

All 2006 2005 2004 Other

All Journal Article (50 results)

  • [Journal Article] Reflection groups of geodesic spaces and Coxeter groups2006

    • Author(s)
      T.Hosaka
    • Journal Title

      Topology and its Applications 153

      Pages: 1860-1866

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Existence theorems and periodic solutions of neutral difference equations2006

    • Author(s)
      T.Furumochi, T.Tsuchie, H.Wada
    • Journal Title

      Cubo Mathematical Journal 8

      Pages: 35-46

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Liapunov functions and boundedness in difference equations2006

    • Author(s)
      T.Furumochi, K.Hishitani, K.Tsuchihashi
    • Journal Title

      Dynamics of Continuous, Discrete and Impulsive Systems 2

      Pages: 331-339

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Reflection groups of geodesic spaces and Coxeter groups2006

    • Author(s)
      T.Hosaka
    • Journal Title

      Topology and its Applications 153(no.11)

      Pages: 1860-1866

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Existence theorems and periodic solutions of neutral difference equations2006

    • Author(s)
      T.Furumochi, T.Tsuchie, H.Wada
    • Journal Title

      Cubo Mathematical Journal 8-3

      Pages: 35-46

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Liapunov functions and boundedness in difference equations, Dynamics of Continuous2006

    • Author(s)
      T.Furumochi, K.Hishitani, K.Tsuchihashi
    • Journal Title

      Discrete and Impulsive Systems 2

      Pages: 331-339

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Reflection groups of geodesic spaces and Coxeter groups2006

    • Author(s)
      T.Hosaka
    • Journal Title

      Topology and its Applications 153・11

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Existence theorems and periodic solutions of neutral difference equations2006

    • Author(s)
      T.Furumochi, T.Tsuchie, H.Wada
    • Journal Title

      Cubo Mathematical Journal 8・3

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Strong transitive and graph maps2005

    • Author(s)
      K.Yokoi
    • Journal Title

      Bulletin of the Polish Academy of Sciences, Mathematics 53

      Pages: 377-388

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Coxeter systems with two-dimensional Davis-Vinverg complexes2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Journal of Pure and Applied Algebra 197

      Pages: 159-170

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Strong reflection rigidity of Coxeter systems of dihedral groups2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Houston Journal of Mathematics 31

      Pages: 37-41

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Addendum to "Dense subsets of the boundary of a Coxeter systems"2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Proceedings of the American Mathematical Society 133

      Pages: 3745-3747

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On dense orbits in the boundary of a Coxeter system2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Journal of Mathematics of Kyoto University 45・3

      Pages: 627-631

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Real hypersurfaces some of whose geodesies are plane curves in nonflat complex space form2005

    • Author(s)
      T.Adachi, M.Kimura, S.Maeda
    • Journal Title

      Tohoku Mathematical Journal 57

      Pages: 223-230

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Congruence classes of Frenet curves in complex quadrics2005

    • Author(s)
      M.Kimura, M.Ortega
    • Journal Title

      Journal of Geometry 83

      Pages: 121-136

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of nonlinear functional differential equations by Schauder's theorem2005

    • Author(s)
      T.A.Burton, T.Furumochi
    • Journal Title

      Nonlinear Analysis 63

      Pages: 217-224

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stabilities in FDEs by Schauder's theorem2005

    • Author(s)
      T.Furumochi
    • Journal Title

      Nonlinear Analysis 63

      Pages: 217-224

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Strong transitivity and graph maps, Bulletin of the Polish Academy of Sciences2005

    • Author(s)
      K.Yokoi
    • Journal Title

      Mathematics 53

      Pages: 377-388

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Coxeter systems with two-dimensional Davis-Vinberg complexes2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Journal of Pure and Applied Algebra 197

      Pages: 159-170

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] Addendum to "Dense subsets of the boundary of a Coxeter system"2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Proceedings of the American Mathematical Society 133

      Pages: 3745-3747

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On dense orbits in the boundary of a Coxeter system2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Journal of Mathematics of Kyoto University 45(no.3)

      Pages: 627-631

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Real hypersurfaces some of whose geodesics are plane curves in nonflat complex space form2005

    • Author(s)
      T.Adachi, M.Kimura, S.Maeda
    • Journal Title

      Tohoku Mathematical Journal 57

      Pages: 223-230

    • NAID

      110001232644

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of nonlinear functional differential equations by Schauder's theorem2005

    • Author(s)
      T.A.Burton, T.Furumochi
    • Journal Title

      Nonlinear Studies 12-1

      Pages: 73-84

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Strong reflection rigidity of Coxeter systems of dihedral groups2005

    • Author(s)
      T.Hosaka
    • Journal Title

      Houston Journal of Mathematics 31(1)

      Pages: 37-41

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Asymptotic behavior of nonlinear functional differential equations by Schauder's theorem2005

    • Author(s)
      T.A.Burton, T.Furumochi
    • Journal Title

      Nonlinear Studies 12

      Pages: 73-84

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Holomorphic helix of proper order 3 on a complex hyperbolic plane2005

    • Author(s)
      T.Adachi, S.Maeda
    • Journal Title

      Topology Appl. 146

      Pages: 201-207

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The interior of the limit set of groups2004

    • Author(s)
      T.Hosaka
    • Journal Title

      Houston Journal of Mathematics 30

      Pages: 705-721

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Dense subsets of the boundary of a Coxeter groups2004

    • Author(s)
      T.Hosaka
    • Journal Title

      Proceedings of the American Mathematical Society 132

      Pages: 3441-3448

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The behavior of dimension functions on unions of closed subsets2004

    • Author(s)
      M.Charalambous, V.Chatyrko, Y.Hattori
    • Journal Title

      Journal of the Mathematical Society of Japan 56

      Pages: 489-501

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stability in Volterra difference equations on a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagamuchi
    • Journal Title

      Fields Institute Communications 42

      Pages: 159-176

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of some functional differential equations by Schauder's theorem2004

    • Author(s)
      T.Furumochi
    • Journal Title

      Proc. 7^<th> coll. QTDE 10

      Pages: 1-11

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Volterra Difference equations, on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Japanese Journal of Mathematics 30

      Pages: 387-412

    • NAID

      10014334745

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Journal of Difference Equations and Applications 10

      Pages: 1201-1214

    • NAID

      120005587462

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Dense subsets of the boundary of a Coxeter system2004

    • Author(s)
      T.Hosaka
    • Journal Title

      Proceedings of the American Mathematical Society 132

      Pages: 3441-3448

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The behavior of dimension functions on unions of closed subsets2004

    • Author(s)
      M.Charalambous, V.Chatyrko, Y.Hattori
    • Journal Title

      Journal of the Mathematical Society of Japan 56(No.3)

      Pages: 489-501

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stabilities in Volterra difference equations or a Banach space2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Fields Institute Communications 42

      Pages: 159-176

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Asymptotic behavior of some functional differential equations by Schauder's theorem2004

    • Author(s)
      T.Furumochi
    • Journal Title

      Proc. 7th Coll. QTDE 10

      Pages: 1-11

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Japanese Journal of Mathematics 30-2

      Pages: 387-412

    • NAID

      10014334745

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A generalization of Wiener's lemma and its application to Volterra difference equations on a Banach2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Journal of Difference Equations and Applications 10

      Pages: 1201-1214

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The interior of the limit set of groups2004

    • Author(s)
      T.Hosaka
    • Journal Title

      Houston J.Math 30

      Pages: 705-721

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Dense subsets of the boundary of a Coxeter system2004

    • Author(s)
      T.Hosaka
    • Journal Title

      Proc.Amer.Math.Soc. 132

      Pages: 3441-3448

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The behaviour of dimension functions on unions of closed subsets2004

    • Author(s)
      M.Charalambous, V.Chatyrko, Y.Hattori
    • Journal Title

      J.Math.Soc.Japan 56

      Pages: 489-501

    • NAID

      10013123053

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Volterra difference equations on a Banach space and abstract differential equations with piecewise continuous delays2004

    • Author(s)
      T.Furumochi, S.Murakami, Y.Nagabuchi
    • Journal Title

      Japan J.Math. 30

      Pages: 387-412

    • NAID

      10014334745

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Dense periodicity on graphs

    • Author(s)
      K.Yokoi
    • Journal Title

      Rocky Mountain Journal of Mathematics (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Dense periodicity on graphs

    • Author(s)
      K.Yokoi
    • Journal Title

      Rocky Mountain Journal of Mathematics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Partitions of spaces by locally compact subspaces

    • Author(s)
      V.A.Chatyrko, Y.Hattori, H.Ohta
    • Journal Title

      Houston Journal of Mathematics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] There is no upper bound of small transfinite compactness degree in metrizable spaces

    • Author(s)
      V.A.Chatyrko, Y.Hattori
    • Journal Title

      Topology and its Applications (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Dense periodicity on graphs

    • Author(s)
      K.Yokoi
    • Journal Title

      Rocky Mountain Journal of Mathematics (印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] There is no upper bound of small transfinite compactness degree in metrizable spaces

    • Author(s)
      V.A.Chatyrko, Y.Hattori
    • Journal Title

      Topology and its Applications (印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Strong transitivity and graph maps

    • Author(s)
      K.Yokoi
    • Journal Title

      Bulletin of the Polish Academy of Sciences, Mathematics (印刷中)

    • Related Report
      2005 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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