• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Exceptional minimal sets of codimension two on flows

Research Project

Project/Area Number 15540078
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

NAKAYAMA Hiromichi  Hiroshima University, Faculty of Integrated Arts and Sciences, Associate Professor, 総合科学部, 助教授 (30227970)

Co-Investigator(Kenkyū-buntansha) MATSUMOTO Shigenori  Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (80060143)
INABA Takashi  Chiba University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (40125901)
SHIBATA Tetsutaro  Hiroshima University, Graduate Scholl of Engineering, Professor, 大学院・工学研究科, 教授 (90216010)
吉田 敏男  広島大学, 総合化学部, 教授 (10033854)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordstopological dynamics / exceptional minimal set
Research Abstract

1.Construction of surface diffeomorphisms with exceptional minimal sets
In 1995, McSwiggen constructed a surface diffeomorphism with a locally connected exceptional minimal set. He inserted a cylindrical hole along a leaf of the strong unstable foliation of a 3-dimensional hyperbolic toral automorphism. We constructed a new example from a 3-dimensional projectively Anosov diffeomorphism.
2.Exceptional minimal sets for group actions on surfaces
In particular, we studied exceptional minimal sets of group actions on the sphere. In the case of hyperbolic groups, it is well known that there are many shapes of exceptional minimal sets. Then we consider the problem what is the easiest group which acts on a surface with a complicated minimal sets. We showed that the exceptional minimal set of an action of a nilpotent group is not homeomorphic to the Siepinski carpet. Furthermore, in the case of the fundamental groups of torus bundles over the circle, we obtain some partial results.
3.Minimal flows of 3-dimensional manifolds
On minimal flows, we investigated their infinitesimal flows and projective flows, we obtain the following dynamical properties :
(1)We used Zimmer's theory in order to obtain invariant fiber measures of projective flows, and deduced several topologaical properties of the original flows.
(2)We investigated minimal flows whose projective flows have exactly two minimal sets, and we showed that it is topologically equivalent to an irrational flow if its projective flow has more than three minimal sets. Furthermore, there is a bundle section separating the minimal sets if there are exactly two minimal sets.
(3)Contreras obtained important results on weakly partially hyperbolic flows. We used his theory to the projective flows and proved the existence of the "upper" orbits and the "lower" orbits of the projective flow if it has exactly two minimal sets.

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (64 results)

All 2006 2005 2004 2003 Other

All Journal Article (59 results) Publications (5 results)

  • [Journal Article] The power of the tangent bundle of the real projective space, its complexification and extendibility2006

    • Author(s)
      T.Kobayashi
    • Journal Title

      Proc. Amer. Math. Soc. 134・1

      Pages: 303-310

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The power of the tangent bundle of the real projective space, its complexification and extendibility.2006

    • Author(s)
      Kobayashi, Teiichi
    • Journal Title

      Proc.Amer.Math.Soc. 134,no.1

      Pages: 303-310

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Minimal sets and chain recurrent sets of projective flows induced from minimal flows on 3-manifolds2005

    • Author(s)
      H.Nakayama
    • Journal Title

      Discrete Contin. Dynam. Systems-Series A 12・4

      Pages: 629-638

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Ends of leaves of Lie foliations2005

    • Author(s)
      G.Hector
    • Journal Title

      J. Math. Soc. Japan 57・3

      Pages: 753-779

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Precise asymptotic properties of solutions to two-parameter elliptic eigenvalue problems in a ball2005

    • Author(s)
      T.Shibata
    • Journal Title

      Advanced Nonlinear Studies 5

      Pages: 33-56

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic shapes of solutions to nonlinear eigenvalue problems2005

    • Author(s)
      T.Shibata
    • Journal Title

      Electronic Journal of Differential Equations 2005 37

      Pages: 1-16

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic expansion of solutions to nonlinear elliptic eigenvalue problems2005

    • Author(s)
      T.Shibata
    • Journal Title

      Proceedings of the American Mathematical Society 133

      Pages: 2597-2604

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Minimal sets and chain recurrent sets of projective flows induced from minimal flow on 3-manifolds2005

    • Author(s)
      H.Nakayama
    • Journal Title

      Discrete Contin.Dynam.Systems - Series A 12-4

      Pages: 629-638

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Ends of leaves of Lie foliations2005

    • Author(s)
      G.Hector
    • Journal Title

      J.Math.Soc.Japan 57,no.3

      Pages: 753-779

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic shapes of solutions to nonlinear eigenvalue problems2005

    • Author(s)
      T.Shibata
    • Journal Title

      Electronic Journal of Differential Equations 2005, No.37

      Pages: 1-16

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic expansion of solutions to nonlinear elliptic eigenvalue problems,2005

    • Author(s)
      T.Shibata
    • Journal Title

      Proceedings of the American Mathematical Society 133

      Pages: 2597-2604

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Minimal sets and chain recurrent sets of projective flows induced from minimal flows on 3-manifolds2005

    • Author(s)
      H.Nakayama
    • Journal Title

      Discrete Contin.Dynam.Systems-Series A 12・4

      Pages: 629-638

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Precise asymptotic properties of solutions to two-parameter elliptic, eigenvalue problems in a ball2005

    • Author(s)
      T.Shibata
    • Journal Title

      Advanced Nonlinear Studies 5

      Pages: 33-56

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Asymptotic shapes of solutions to nonlinear eigenvalue problems2005

    • Author(s)
      T.Shibata
    • Journal Title

      Electronic Journal bf Differential Equations 2005 37

      Pages: 1-16

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Minimal sets and chain recurrent sets of projective flows induced from minimal flows on 3-manifolds2005

    • Author(s)
      H.Nakayama
    • Journal Title

      Discrete Contin.Dynam.Systems - Series A 12-4

      Pages: 629-638

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Invariant fiber measures of angular flows and the Ruelle invariant2004

    • Author(s)
      T.Inaba
    • Journal Title

      J. Math. Soc. Japan 56・1

      Pages: 17-29

    • NAID

      10013122519

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Locally connected exceptional minimal sets of surface homeomorphisms2004

    • Author(s)
      A.Bi's
    • Journal Title

      Ann. Inst. Fourier (Grenoble) 54・3

      Pages: 711-732

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stably extendible vector bundles over real projective spaces2004

    • Author(s)
      T.Kobayashi
    • Journal Title

      Adv. Stud. Contemp. Math. (Kyungshang) 8・2

      Pages: 165-176

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Extendibility and stable extendibility of vector bundles over lens spaces mod 42004

    • Author(s)
      T.Kobayashi
    • Journal Title

      Men. Fac. Sci. Kochi Univ. Ser. A Math. 25

      Pages: 23-36

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Precise spectral asymptotics for logistic equations of population dynamics2004

    • Author(s)
      T.Shibata
    • Journal Title

      Bulletin of London Mathematical Society 36

      Pages: 59-64

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The steepest point of the boundary layers of singularly perturbed semilinear elliptic problems2004

    • Author(s)
      T.Shibata
    • Journal Title

      Transaction of the America Mathematical Society 356

      Pages: 2123-2135

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Three-term spectral asymptotics for the perturbed simple pendulum problems2004

    • Author(s)
      T.Shibata
    • Journal Title

      Differential Integral Equations 17

      Pages: 215-226

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic expansion of the variational eigencurve for two-parameter simple pendulum type equations2004

    • Author(s)
      T.Shibata
    • Journal Title

      Nonlinear Analysis 58

      Pages: 425-440

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic formula for eigenvalues of simple pendulum Problems2004

    • Author(s)
      T.Shibata
    • Journal Title

      Asymptotic analysis 40

      Pages: 83-91

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Variational method for precise asymptotic formulas for nonlinear eigenvalue problems2004

    • Author(s)
      T.Shibata
    • Journal Title

      Results in Mathematics 46

      Pages: 130-145

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Invariant fiber measures of angular flows and the Ruelle invariant2004

    • Author(s)
      T.Inaba
    • Journal Title

      J.Math.Soc.Japan 56-1

      Pages: 17-29

    • NAID

      10013122519

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Locally connected exceptional minimal sets of surface homeomorphisms2004

    • Author(s)
      A.Bi's
    • Journal Title

      Ann.Inst.Fourier (Grenoble) 54-3

      Pages: 711-732

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stably extendible vector bundles over real projective spaces.2004

    • Author(s)
      Kobayashi, Teiichi
    • Journal Title

      Adv.Stud.Contemp.Math. (Kyungshang) 8,no.2

      Pages: 165-176

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Extendibility and stable extendibility of vector bundles over lens spaces mod 4.2004

    • Author(s)
      Kobayashi, Teiichi
    • Journal Title

      Mem.Fac.Sci.Kochi Univ.Ser.A Math. 25

      Pages: 23-36

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The stccpcst point of the boundary layers of singularly perturbed semilinear elliptic problems2004

    • Author(s)
      T.Shibata
    • Journal Title

      Transactions of the American Mathematical Society 356

      Pages: 2123-2135

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic formula for eigenvalues of simple pendulum problems2004

    • Author(s)
      T.Shibata
    • Journal Title

      Asymptotic analysis 40

      Pages: 83-91

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Variational method for precise asymptotic formulas for nonlinear eigenvalue problems,2004

    • Author(s)
      T.Shibata
    • Journal Title

      Results in Mathematics 46,no.1-2

      Pages: 130-145

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Locally connected exceptional minimal sets of surface homeomorphisms2004

    • Author(s)
      A.Bis
    • Journal Title

      Ann.Inst.Fourier(Grenoble) 54-3

      Pages: 711-732

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Extendibility and stable extendibility of vector bundles over lens spaces mod 42004

    • Author(s)
      T.Kobayashi
    • Journal Title

      Mem.Fac.Sci.Kochi Univ.(Math.) 25

      Pages: 23-36

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stably extendible vector bundles over real projective spaces2004

    • Author(s)
      T.Kobayashi
    • Journal Title

      Adv.Stud.Contemp.Math. 8

      Pages: 165-176

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stable extendibility of vector bundles over real projective spaces and determination of the Schwarzenberger number β(k)2003

    • Author(s)
      T.Kobayashi
    • Journal Title

      Mem. Fac. Sci. Kochi Univ. Ser. A Math. 24

      Pages: 19-35

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Extendible and stably extendible vector bundles over real projective spaces.2003

    • Author(s)
      T.Kobayashi
    • Journal Title

      J. Math. Soc. Japan 55・4

      Pages: 1053-1059

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stable extendibility of vector bundles over real projective spaces and bounds for the Schwarzenberger numbers β(k)2003

    • Author(s)
      T.Kobayashi
    • Journal Title

      Hiroshima Math. J. 33・3

      Pages: 371-377

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Leafwise cohomology and rigidity of certain Lie group actions2003

    • Author(s)
      S.Matsumoto
    • Journal Title

      Ergodic Theory and Dynamical Systems 23

      Pages: 1839-1866

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Open Engel manifolds admitting compact characteristic leaves2003

    • Author(s)
      T.Inaba
    • Journal Title

      Bulletin of Australian Math. Soc. 68

      Pages: 213-219

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The effect of the variational framework on the spectral asymptotics for two-parameter nonlinear eigenvalue problems2003

    • Author(s)
      T.Shibata
    • Journal Title

      Mathematics Nachrichten 248/249

      Pages: 168-184

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Precise asymptotic formulas for variational eigencurves of semilinear two-parameter elliptic eigenvalue problems2003

    • Author(s)
      T.Shibata
    • Journal Title

      Annali di Matematica Pura ed Applicata 182

      Pages: 211-229

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic formulas for boundary layers and eigencurves for nonlinear elliptic eigenvalue problems2003

    • Author(s)
      T.Shibata
    • Journal Title

      Communications in Partial Differential Equations 28

      Pages: 581-600

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic formulas and critical exponents for two-parameter nonlinear eigenvalue problems2003

    • Author(s)
      T.Shibata
    • Journal Title

      Abstract and Applied Analysis 2003

      Pages: 671-684

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic expansion of the boundary layers of the perturbed simple pendulum problems2003

    • Author(s)
      T.Shibata
    • Journal Title

      Journal of Mathematical Analysis and Applications 283

      Pages: 431-439

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the global rigidity of split Anosov R^n-actions2003

    • Author(s)
      S.Matsumoto
    • Journal Title

      J. Math. Soc. Japan 55

      Pages: 39-46

    • NAID

      10011477915

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stable extendibility of vector bundles over real projective spaces and determination of the Schwarzenberger number β(k)2003

    • Author(s)
      Kobayashi, Teiichi
    • Journal Title

      Mem.Fac.Sci.Kochi Univ.Ser.A Math. 24

      Pages: 19-35

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Extendible and stably extendible vector bundles over real projective spaces.2003

    • Author(s)
      Kobayashi, Teiichi
    • Journal Title

      J.Math.Sco.Japan 55,no.4

      Pages: 1053-1059

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stable extendibility of vector bundles over real projective spaces and bounds for the Schwarzenberger numbers β(k)2003

    • Author(s)
      Kobayashi, Teiichi
    • Journal Title

      Hiroshima Math.J. 33,no.3

      Pages: 371-377

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Leafwise cohomology and rigidity of certain Lie group actions.2003

    • Author(s)
      S.Matsumoto
    • Journal Title

      Ergodic Theory and Dynamical Systems 23

      Pages: 1839-1866

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the global rigidity of split Anosov R^n-actions.2003

    • Author(s)
      S.Matsumoto
    • Journal Title

      J.Math.Soc.Japan 55

      Pages: 39-46

    • NAID

      10011477915

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Open Engel manifolds admitting compact characteristic leaves2003

    • Author(s)
      Takashi Inaba
    • Journal Title

      Bulletin of Australian Math.Soc. 68

      Pages: 213-219

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The effect of the variational framework on the spectral asymptotics for two-parameter nonlinear eigenvalue problems2003

    • Author(s)
      T.Shibata
    • Journal Title

      Mathematische Nachrichten 248/249

      Pages: 168-184

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Precise asymptotic formulas for variational eigencurves of semilinear two-parameter elliptic eigenvalue problems2003

    • Author(s)
      T.Shibata
    • Journal Title

      Annali di Matematica Pura ed.Applicata 182

      Pages: 211-229

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Asymptotic formulas and critical exponents for two-parameter nonlinear eigenvalue problems.2003

    • Author(s)
      T.Shibata
    • Journal Title

      Abstract and Applied Analysis 2003

      Pages: 671-684

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Fiberwise divergent orbits of projective flows with exactly two minimal sets

    • Author(s)
      H.Nakayama
    • Journal Title

      Pacific Journal of Mathematics (掲載決定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Fiberwise divergent orbits of projective flows with exactly two minimal sets

    • Author(s)
      H.Nakayama
    • Journal Title

      Pacific Journal of Mathematics (accepted)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Fiberwise divergent orbits of projective flows with exactly two minimal sets

    • Author(s)
      H.Nakayama
    • Journal Title

      Pacific Journal of Mathematics (掲載決定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The power of the tangent bundle of the real projective space, its complexification and extendibility

    • Author(s)
      T.Kobayashi
    • Journal Title

      Proc.Amer.Math.Soc. (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Publications] T.Inaba: "Invariant fiber measures of angular flows and the Ruelle invariant"J.Math.Soc.Japan. 56・1. 17-29 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] A, Bi's: "Locally connected exceptional minimal sets of surface homeomorphisms"Ann.Inst.Fourier (Grenoble). (印刷中). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Teiichi Kobayashi: "Extendible and stably extendible vector bundles over real projective spaces"J.Math.Soc.Japan. 55・4. 1053-1059 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Teiichi Kobayashi: "Stable extendibility of vector bundles over real projective spaces and bounds for the Schwarzenberger numbers β(k)"Hiroshima Math.J.. 33・3. 371-377 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Teiichi Kobayashi: "Extendibility and stable extendibility of vector bundles over lens spaces mod 4"Mem.Fac.Sci.Kochi Univ.(Math.). 25. 21-34 (2004)

    • Related Report
      2003 Annual Research Report

URL: 

Published: 2003-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi