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Synthetic Study of Foliations and Dynamical Systems

Research Project

Project/Area Number 09440042
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

MATUMOTO Shigenori  Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (80060143)

Co-Investigator(Kenkyū-buntansha) KOJIMA Sadayoshi  Tokyo Institute of Technology, Graduate school of Information Science and Engineering, 大学院・情報理工学研究科, 教授 (90117705)
TSUBOI Takashi  University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (40114566)
INABA Takashi  Chiba University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (40125901)
MINAKAWA Hiroyuki  Hirosaki University, Faculty of Education, Assistant Professor, 教育学部, 助教授 (30241300)
NAKAYAMA Hiromichi  Hiroshima University, Faculty of Integarated Arts and Sciences, Lecturer, 総合科学部, 講師 (30227970)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥6,200,000 (Direct Cost: ¥6,200,000)
Fiscal Year 1999: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1998: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1997: ¥2,300,000 (Direct Cost: ¥2,300,000)
Keywordsfoliations / area preserving maps / rotation number / rotation vector / symplectic diffeomorphism / Hamiltonian flow / holonomy group / transverse measure / 面積保存同相写像 / シンプレクティック微分同相 / 周期軌道 / 位相的エントロピー / 不動点指数 / 極小集合 / 余次元1葉層 / エルゴード的測度 / イソトピー
Research Abstract

Dynamical Systems without Minimal Sets There exists a flow without minimal set on a certain surface of infinite type. Also there is a diffeomorphism without minimal set on an open annulus.
Transverse Intersection of Two Foliations on 3-manifolds The stable and unstable foliations of the suspension Anosov flow are shown to intersect transversely in an unique way. On the countrary, there are nonstandard way of intersection of the stable and unstable foliations of the geodesic flows of hyperbolic surfaces.
Flows on 3-manifolds Consider a nonsigular vector field X on a 3-manifold M and the flow φ defined by X. The differential of the flow defines a flow ψ on the projectived normal bundle P of the flow X. Thus the invariant measure ν of ψ on P gives rise to an invariant measure μ of φ on M. We showed that one of the followings occurs. (1) For μ-a.e. x ∈ M, Supp(ν) ∩ PィイD2xィエD2 is one point. (2) For μ-a.e. x ∈ M, Supp(ν) ∩ PィイD2xィエD2 consists of two points. (3) For μ-a.e. x ∈ M. PィイD2xィエD2 is contained in Supp(ν).
We also showed that for the lift of ψ to the cyclic convering of P which unfolds the fibers, one of the followings holds. (1) All the orbits are bounded. (2) All the orbits are proper. (3) There is a dense orbits.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • Research Products

    (37 results)

All Other

All Publications (37 results)

  • [Publications] 松元重則: "Arnold Conjecture for surface homeomorphisms"Topology and its applications. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 稲葉尚志: "Expansivily pseudoleaf tracing pooperty and senie-stability of foliation's"Tokyo Journal of Mathematics. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 稲葉尚志: "An example of a flow ona noncompudt surface which has no minimal set"Ergodic Theory and Dynamical Systems. 19. 31-33 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 平井俊: "The Calabi invariant and the Euler class"Transaction of the American Mathematical Society. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 小島定吉・藤井道彦: "Flexible boundaries in deformations of hyperbolic 3-manifolds"Osaka Journal of Mathematics. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 小島定吉: "Deformation of hyperbolic 3-manifolds"Journal of Differential Geometry. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 小島定吉(監訳): "3次元幾何学とトポロジー"培風館. 309 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 三松佳彦: "3次元接触トポロジー"日本数学会日本語メモアール(発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Shigenori Matsumoto: "Arnold conjecture for surface homeomorphisms"Topology and its applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takashi Inaba: "Expansivity, pseudoleaf tracing property and semistability of foliations"Tokyo Journal of Mathematics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takashi Inaba: "An example of a flow on a noncompact surface which has no minimal set"Ergodic Theory and Dynamical systems. 19. 31-33 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takashi Tsuboi: "The Calabi invariant and the Euler class"Transaction of the American Mathematical Socienty. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Sadayoshi Kojima and Michihiko Fujii: "Flexible boundaries in deformations of hyperbolic 3-manifolds"Osaka Journal of Mathematics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Sadayoshi Kojima: "Deformation of hyperbolic 3-manifolds"Journal of Differential Geomety. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Sadayoshi Kojima: "3-dimensional geometry and Topology"W. Thurston, Head Translator, Baihukan. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yoshihiko Mitsumatsu: "3-dimensional contct topology"To appear in Memoire of the Mathematical Society of Japan (In Japanese).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 松元重則: "Arnold Conjecture for surface homeomorphisms"Topology and its applications. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 稲葉尚志: "Expansirity,pseudoleaf tracing property and semi-stability of foliations"Tokyo Journal of Mathematics. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 稲葉尚志: "An example of a flow on a noncompact surface which has no minimal set"Ergodic Theory and Dynamical Systems. 19. 31-33 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 坪井俊: "The Calabi invariant and the Euler class"Transaction of the Americacl Mathematical Society. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 小島定吉-藤井道彦: "Flexible boundaries in deformations of hyperbolic 3-manifolds"Osaka Journal of Mathematics. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 小島定吉: "Deformations of hyperbolic 3-manifolds"Journal of Differential Geometry. (発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 小島定吉(監訳): "3次元幾何学とトポロジー"培風館. 309 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 三松佳彦: "3次元接触トポロジー"日本数学会日本語メモアール(発表予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 松本重則: "Arnold conjecture for surface homeomorphisms" Topology and its Applications. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 稲葉尚志: "An example of a flow on a noncompact surface without mininal set" Ergodic Theory and Dynamical Systems. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 坪井俊: "Irrational foliations of S^3×S^3" Hokkaido Mathematical Journal. 27. 605-623 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 坪井 俊: "The Calabi Invariant and the Euler class" Tramsacfions of the American Mathematical Sociefies. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 小島定吉: "Hyperbolic 3-manifolds singular along Knots" Chaos, Solirons and Fractals. 9. 765-777 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 小島定吉: "Doformations of hyperbolic 3-cone-manifolds" Journal of Differendial Geometry. 発表予定.

    • Related Report
      1998 Annual Research Report
  • [Publications] 小島定吉: "トポロジー入門" 共立出版, (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 松元重則: "Rotation sets of surface homeomorphisms" Boletim da Sociedade Brasifeira de Matematica. 28. 89-101 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 松元重則、A.El.Kacimi T.Moussa: "Currents invariants by a Kleinian group" Hokkaido Mathematical Journal. 26. 177-202 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 松元重則・中山裕道: "On ν-distal flows on 3-manifolds" Bulletin of the London Mathematical Sociefy. 29. 609-616 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 稲葉尚志: "An example of a flow on a noncompact surface without minimal set." Ergodic Theory and Dynamical Systems. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 小島定吉,藤井道彦: "Flexible boundaries in Deformations of hyperbolic 3-manifolds" Osaka Journal of Mathematics. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 皆川宏之: "Realization of Ghys mequalities" Topology. 36. 775-781 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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