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Study of functional analytic methods in dynamical system theory

Research Project

Project/Area Number 18340044
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKyushu University (2007-2009)
Hokkaido University (2006)

Principal Investigator

TSUJII Masato  Kyushu University, 大学院・数理学研究院, 教授 (20251598)

Co-Investigator(Kenkyū-buntansha) 新居 俊作  九州大学, 数理学研究院, 准教授 (50282421)
石井 豊  九州大学, 数理学研究院, 准教授 (20304727)
由利 美智子  北海道大学, 大学院・理学研究院, 教授 (70174836)
Co-Investigator(Renkei-kenkyūsha) ISHII Yutaka  九州大学, 大学院・数理学研究院, 准教授 (20304727)
NII Shunsaku  九州大学, 大学院・数理学研究院, 准教授 (50282421)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥14,970,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥2,670,000)
Fiscal Year 2009: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2008: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2007: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2006: ¥3,400,000 (Direct Cost: ¥3,400,000)
Keywords力学系 / 関数解析 / エルゴード理論 / カオス / ゼータ関数 / 転移作用素 / スペクトル / 量子カオス / 双曲力学系
Research Abstract

We studied functional analytic methods in dynamical systems theory and ergodic theory. For hyperbolic and partially hyperbolic dynamical systems, we constructed function spaces on the phase space adapted to the system so that the corresponding transfer operators have good spectral properties on them. As an application, we get precise results on Ruelle-Pollicott resonance and analytic properties of dynamical zeta functions especially for expanding semi-flows and geodesic flows on negatively curved manifolds.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (50 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (32 results) (of which Peer Reviewed: 25 results) Presentation (14 results) Remarks (4 results)

  • [Journal Article] Homotopy shadowing. (with J. ~Smillie)2010

    • Author(s)
      Ishii, Yutaka
    • Journal Title

      Amer. J. Math 132(In press)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Homotopy shadowing2010

    • Author(s)
      石井豊, J.Smilie
    • Journal Title

      Amer. J. Math. (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees.2009

    • Author(s)
      Ishii, Yutaka
    • Journal Title

      Adv. Math 220,no.4

      Pages: 985-1022

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] "Julia sets and chaotic tunneling I". (with A. ~Shudo and K. ~S. ~Ikeda)2009

    • Author(s)
      Ishii, Yutaka
    • Journal Title

      J. Phys. A: Math. Theor 42

      Pages: 265101-26

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] "Julia sets and chaotic tunneling II". (with A. ~Shudo and K. ~S. ~Ikeda)2009

    • Author(s)
      Ishii, Yutaka
    • Journal Title

      J. Phys. A: Math. Theor 42

      Pages: 265102-34

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcations of stationary solutions with triple junctions in phase separation problems-A new view of bifurcation analysis-2009

    • Author(s)
      Nii, Shunsaku
    • Journal Title

      in Physica D 238

      Pages: 1050-1055

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcations of stationary solutions with triple junctions in phase separation problems --A new view of bifurcation analysis--2009

    • Author(s)
      新居俊作
    • Journal Title

      Physica D 238

      Pages: 1050-1055

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Julia sets and chaotic tunneling. I, II2009

    • Author(s)
      石井豊
    • Journal Title

      Journal of Physics A 42

      Pages: 265101-265102

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectra of differentiable hyperbolic maps.2008

    • Author(s)
      Baladi, Viviane; Tsujii, Masato
    • Journal Title

      Traces in number theory, geometry and quantum fields, 1-21, Aspects Math., E38, Friedr. Vieweg, Wiesbaden

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dynamical determinants and spectrum for hyperbolic diffeomorphisms2008

    • Author(s)
      Baladi, Viviane; Tsujii, Masato
    • Journal Title

      Geometric and probabilistic structures in dynamics, 29-68, Contemp. Math. 469

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decay of correlations in suspension semi-flows of angle-multiplying maps2008

    • Author(s)
      Tsujii, Masato
    • Journal Title

      Ergodic Theory Dynam. Systems no.1

      Pages: 291-317

    • NAID

      120006459456

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic polynomial diffeomorphisms of C^2. I: A non-planar map.2008

    • Author(s)
      Ishii, Yutaka
    • Journal Title

      Adv. Math 218,no.2

      Pages: 417-464

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] An infinite-dimensional Evans function theory for elliptic boundary value problems2008

    • Author(s)
      Deng, Jian; Nii, Shunsau
    • Journal Title

      J. Differential Equations 244,no.4

      Pages: 753-765

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decay of correlations in suspension semi-flows of angle-multiplying maps2008

    • Author(s)
      Tsujii, Masato
    • Journal Title

      Ergodic Theory Dynam.Systems 28no. 1

      Pages: 291-317

    • NAID

      120006459456

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Decay of correlations in suspension semi-flows of angle-multiplying maps.2008

    • Author(s)
      辻井 正人
    • Journal Title

      Ergodic theory and dynamical systems 28-1

      Pages: 291-371

    • NAID

      120006459456

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic polynomial diffeomorphisms of $\Bbb C\sp 2$. I. A non-planar map.2008

    • Author(s)
      石井 豊
    • Journal Title

      Advances in Mathematics 218-2

      Pages: 417-464

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An infinite-dimensional Evans function theory for elliptic boundary value problems2008

    • Author(s)
      新居 俊作, Deng Jian
    • Journal Title

      Journal of Differential Equations 244-4

      Pages: 753-765

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An Infinite-dimensional Evans function theory for elliptic boundary value problems2008

    • Author(s)
      新居 俊作
    • Journal Title

      Jounal of Differential Equations 244

      Pages: 753-765

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Anisotropic Holder and Sobolev spaces for hyperbolic diffeomorphisms2007

    • Author(s)
      Baladi, Viviane; Tsujii, Masato
    • Journal Title

      Ann. Inst. no.1

      Pages: 127-154

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lap number entropy formula for piecewise affine and projective maps in several dimensions. (with D. ~Sands)2007

    • Author(s)
      Sands, Duncan; Ishii, Yutaka
    • Journal Title

      Nonlinearity 20,no.12

      Pages: 2755-2772

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Anisotropic Holder and Sobolev spaces for hyperbolic diffeom orphisms2007

    • Author(s)
      辻井 正人
    • Journal Title

      Annals of Institute Fourier 57

      Pages: 127-154

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lap number entropy formula for piecewise affine and projective maps in several dimensions2007

    • Author(s)
      石井 豊
    • Journal Title

      Nonlinearity 20

      Pages: 2755-2772

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Zeta functions and dynamical systems2006

    • Author(s)
      Liverani, Carlangelo; Tsujii, Masato
    • Journal Title

      Nonlinearity no.10

      Pages: 2467-2473

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Smoothness of solenoidal attractors2006

    • Author(s)
      Avila, Artur; Gouezel, Sebastien; Tsujii, Masato
    • Journal Title

      Discrete Contin. Dyn. Syst

      Pages: 21-35

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infinite-dimensional Evans function theory for elliptic eigenvalue problems in a channel2006

    • Author(s)
      Deng, Jian; Nii, Shunsaku
    • Journal Title

      J. Differential Equations no.1,225

      Pages: 57-89

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Zeta functions and dynamical systems2006

    • Author(s)
      Liverani, Carlangelo ; Tsujii, Masato
    • Journal Title

      Nonlinearity 19 no. 10

      Pages: 2467-2473

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Smoothness of solenoidal attractors.Discrete Contin2006

    • Author(s)
      Avila, Artur ; Gouezel, Sebastien ; Tsujii, Masato
    • Journal Title

      Dyn. Syst. 15 no. 1

      Pages: 21-35

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Zeta functions and dynamical systems2006

    • Author(s)
      Tsujii, M.
    • Journal Title

      Nonlinearity 19

      Pages: 2467-2473

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Smoothness of solenoidal attractor2006

    • Author(s)
      Tsujii, M.
    • Journal Title

      Discrete and continuous dynamical systems 15・1

      Pages: 21-35

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Absolutely continuous invariant measures for multi-dimensional piecewise expanding maps2006

    • Author(s)
      Tsujii, M.
    • Journal Title

      Sugaku expositions 19

      Pages: 19-34

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Quasi-compactness of transfer operators for contact Anosov flows

    • Author(s)
      Tsujii, Masato
    • Journal Title

      (印刷中)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dynamical determinants and spectrum for hyperbolic diffeomorphisms In "Probabilistic and Geometric Structures in Dynamics"

    • Author(s)
      Baladi, Viviane ; Tsujii, Masato
    • Journal Title

      Contemp. Math. (Amer. Math. Soc.), Volume in honour of M. Brin's 60th birthday

    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Functional analytic methods in smooth ergodic theory2010

    • Author(s)
      辻井正人
    • Organizer
      「Dynamics and PDE's」Mittag-Leffler研究所
    • Place of Presentation
      ストックホルム, スウェーデン
    • Related Report
      2009 Final Research Report
  • [Presentation] Functional analytic methods in smooth ergodic theory2010

    • Author(s)
      辻井正人
    • Organizer
      Dynamics and PDE's
    • Place of Presentation
      Mittag-Leffler Institute(Stockholm, Sweden)
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the semi-classical zeta functions for negatively curved manifolds2009

    • Author(s)
      辻井正人
    • Organizer
      MFO
    • Place of Presentation
      Oberwolfach, ドイツ
    • Year and Date
      2009-11-10
    • Related Report
      2009 Final Research Report
  • [Presentation] 半古典ゼーター関数の零点の分布について(可変負曲率多様体の測地流の場合)2009

    • Author(s)
      辻井正人
    • Organizer
      力学系冬の研究集会
    • Place of Presentation
      日本大学軽井沢研修所(軽井沢, 長野)
    • Year and Date
      2009-01-11
    • Related Report
      2009 Final Research Report
  • [Presentation] Quasi-compactness of transfer operators for contact Anosov flows2008

    • Author(s)
      辻井正人
    • Organizer
      Dynamics Days Asia Pacific 5
    • Place of Presentation
      新奈良公会堂, 奈良
    • Year and Date
      2008-09-10
    • Related Report
      2009 Final Research Report
  • [Presentation] Quasi-compactness of transfer operators for contact Anosov flows2008

    • Organizer
      Dynamics Days Asia Pacific 5
    • Place of Presentation
      新奈良公会堂
    • Year and Date
      2008-09-10
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] 負曲率多様体の測地流における相関の減衰2008

    • Organizer
      Dynamics of complex systems 2008
    • Place of Presentation
      北海道大学
    • Year and Date
      2008-09-01
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Quasi-compactness of transfer operators for contact Anosov2008

    • Author(s)
      辻井正人
    • Organizer
      WORKSHOP on HYPERBOLIC DYNAMICAL SYSTEMS WITH SINGULARITIES
    • Place of Presentation
      Irwin Schrodinger Institute, Vienna, オーストリア
    • Year and Date
      2008-06-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Quasi-compactness of transfer operators for contact Anosov2008

    • Organizer
      WORKSHOP on HYPERBOLIC DYNAMICAL SYSTEMS WITH SINGULARITIES
    • Place of Presentation
      Irwin Schrodinger Institute, Vienna
    • Year and Date
      2008-06-24
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Quasi-compactness of transfer operators for contact Anosov flows2008

    • Author(s)
      辻井 正人
    • Organizer
      Hyperbolic dynamical systems
    • Place of Presentation
      Erwin Schrodinger Institute (Vienna, Austria)
    • Year and Date
      2008-06-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Spectrum of transfer operators for hyperbolic lows2008

    • Author(s)
      辻井正人
    • Organizer
      Workshop GREFI-MEFI 2008 "From dynamical systems to statistical mechanics"
    • Place of Presentation
      at CIRM, Marseille, フランス
    • Year and Date
      2008-02-13
    • Related Report
      2009 Final Research Report
  • [Presentation] Spectrum of transfer operators for hyperbolic lows2008

    • Organizer
      Workshop GREFI-MEFI 2008 "From dynamical systems to statistical mechanics"
    • Place of Presentation
      CIRM, Marseille
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Quasi-Compactness of Transfer Operators for Contact Anosov Flows2008

    • Organizer
      CTS workshop on dynamical systems
    • Place of Presentation
      National Tsing-Hua university,Taiwan
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Quasi-compactness of transfer operators for contact Anosov flows2008

    • Author(s)
      辻井 正人
    • Organizer
      From dynamical systems to statistical mechanics
    • Place of Presentation
      CIRM, Marseilie
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://www2.math.kyushu-u.ac.jp/~tsujii/

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www2.math.kyushu-u.ac.jp/~tsujii/

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www2.math.kyushu-u.ac.jp/~tsujii/research.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://hyoka.ofc.kyushu-u.ac.jp/search/details/K003099/index.html

    • Related Report
      2007 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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