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ON THE CHARACTERIZATION OF HOMOCLINIC CLASSES BY MEANS OF THE SHADOWING PROPERTY

Research Project

Project/Area Number 22540218
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionUtsunomiya University

Principal Investigator

SAKAI Kazuhiro  宇都宮大学, 教育学部, 教授 (30205702)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords力学系 / 力学系理論 / 擬軌道尾行性 / ホモクリニッククラス / 双曲性 / 占有的分割
Research Abstract

Since Anosov and Bowen's works, the notion of the pseudo-orbit shadowing property very often appears in the several branches of the theory of dynamical systems, and usually plays an important role in the investigation. The latest developments of the shadowingtheory of dynamical systems are very remarkable; in fact, the shadowing theory is not only a base of numerical study of dynamical systems but also gives rise to lots of important consequences in qualitative theory of dynamical systems. The purpose of this research project is to characterize the dynamical systems or subsystems possessing the shadowing property from view point of the differential geometric theory of dynamical systems.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (12 results)

All 2013 2012 2011 2010

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (7 results) (of which Invited: 1 results)

  • [Journal Article] Shadowing chain transitive sets2013

    • Author(s)
      K. Sakai
    • Journal Title

      to appear in Journal of Difference Equations and Applications

      Volume: 19 Issue: 10 Pages: 1601-1618

    • DOI

      10.1080/10236198.2013.767897

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Regular maps satisfying the specification property2013

    • Author(s)
      K. Moriyasu, K. Sakai and K. Yamamoto
    • Journal Title

      Discrete and Contin. Dynam. Syst.

      Volume: 33 Issue: 7 Pages: 2991-3009

    • DOI

      10.3934/dcds.2013.33.2991

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Diffeomorphisms with the s-limit shadowing property2012

    • Author(s)
      K. Sakai
    • Journal Title

      Dynamical Systems: An International Journal

      Volume: 27 Issue: 4 Pages: 403-410

    • DOI

      10.1080/14689367.2012.691960

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] C^1-stably weakly shadowing homoclinic classes admit dominated splittings2010

    • Author(s)
      S.Gan, K.Sakai, L.Wen
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: 27 Pages: 205-216

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Positively expansive differentiable maps2010

    • Author(s)
      K.Sakai
    • Journal Title

      Acta Mathematica Sinica, English Series

      Volume: 26 Pages: 1839-1846

    • NAID

      110008451459

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Measure-expansive diffeomorphisms, Recent Trends in Ergodic Theory &Dynamical Systems2012

    • Author(s)
      K. Sakai, N. Sumi and K. Yamamoto
    • Organizer
      The Maharaja SayajiraoUniversity of Baroda
    • Place of Presentation
      Vadodara, Gujarat, INDIA
    • Year and Date
      2012-12-28
    • Related Report
      2012 Final Research Report
  • [Presentation] Measure-expansive diffeomorphisms2012

    • Author(s)
      K. Sakai
    • Organizer
      Recent Trends in Ergodic Theory & Dynamical Systems
    • Place of Presentation
      The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, INDIA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Shadowing chain transitive sets2011

    • Author(s)
      K. Sakai
    • Organizer
      北京大学数学教室
    • Place of Presentation
      北京大学,北京,中国
    • Year and Date
      2011-08-26
    • Related Report
      2012 Final Research Report
  • [Presentation] C1-stably weakly shadowing homoclinic classes, Workshop on Dynamical Systems and Applied Mathematics2010

    • Author(s)
      K. Sakai
    • Organizer
      Uniwersytet Jagiellonski
    • Place of Presentation
      Krakow, Polska
    • Year and Date
      2010-10-15
    • Related Report
      2012 Final Research Report
  • [Presentation] C^1-stably weakly shadowing homoclinic classes2010

    • Author(s)
      K.Sakai
    • Organizer
      Workshop on Dynamical Systems and Applied Mathematics
    • Place of Presentation
      Uniwersytet Jagiellonski, Krakow, Polska
    • Year and Date
      2010-10-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] C1-stably weakly shadowing homoclinic classes, Various Aspects of Dynamical Systems, ICM 2010 Satellite Conference2010

    • Author(s)
      K. Sakai
    • Organizer
      The Maharaja SayajiraoUniversity of Baroda
    • Place of Presentation
      Vadodara, Gujarat, INDIA
    • Year and Date
      2010-08-31
    • Related Report
      2012 Final Research Report
  • [Presentation] C^1-stably weakly shadowing homoclinic classes2010

    • Author(s)
      K.Sakai
    • Organizer
      Various Aspects of Dynamical Systems, ICM 2010 Satellite Conference
    • Place of Presentation
      The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, INDIA
    • Year and Date
      2010-08-31
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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