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Study on the Onset and Structures of Chaos from the Standpoint of Statistical Physics

Research Project

Project/Area Number 61540266
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 物性一般(含極低温・固体物性に対する理論)
Research InstitutionKyushu University

Principal Investigator

YOSHIDA Takeshi  Kyushu University, 理学部, 助手 (10037187)

Co-Investigator(Kenkyū-buntansha) OKAMOTO Hisao  Kyushu University, 理学部, 助教授 (50037222)
MORI Hazime  Kyushu University, 理学部, 教授 (90037143)
Project Period (FY) 1986 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1988: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1987: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1986: ¥700,000 (Direct Cost: ¥700,000)
KeywordsPeriodic chaos / Intermittent chaos / Power spectrum of chaos / Multifractal structure / Local expansion rate of chaotic orbit / カオスの統計力学的定式化 / gー相転移 / 一次元写像系 / 奇妙なアトラクター / q-相移転 / テント写像 / ロジスティック写像 / ヘノン写像 / 散逸標準写像 / フラクタル次元 / 一般化次元 / 特異性のスペクトル / リァプノフ指数 / 軌道拡大率に対するスペクトル / 一般化エントロピー / 周期倍化分岐 / 間欠的カオス / 1 / f-スペクトル / エノン写像 / レスラー系 / 減衰強制振子
Research Abstract

The purpose of this project is to reveal characteristic strctures of chaos observed ubiquitously in dissipative dynamical systems and to obtain a clue for constructing the statistical mechanics of chaos from the first principle. We take the standpoint that an essential mechanism of chaos in dissipative systems will be found in low-dimensional discrete time dynamical systems. Thus chaos generated by one- and two-dimensional maps are considered. We started with chaos near its onset point and the characteristic structures of power spectra of orbits in this chaos have been found. Then we proceeded to off-boundary chaos and its characterisic properties were investigated in terms of two quantities: one is the spectrum of singularities characterizing multifractal structures of measures on strange attractors and the other the spectrun of fluctuation of local expansion rates of chaotic orbits. The main results are as follows: 1. The power spectra of periodic chaos which emerges via period-doubling bifurcations show characteristic structures governed by the universal recursion relations derived on the basis of similarities in the process of band-splitting bifurcations of this chaos. 2. The power spectra of intermittent chaos are characterized by a series of peaks and the power low for their envelope, the statistical properties of the duration of laminar motion and the jumps in amplitude and phase by bursts being important factors. 3. The characteristic relations between the spectrum of singularities and the fluctuation spectrum of local expansion rates are obtained for certain kinds of chaos in hyperbolic dynamical systems. 4. Phase transitions associated with anomalous flucturations of local expansion rates are found at bifurcation points of chaos on the basis of the formalism similar to the usual statistical mechanics. 5. Critical exponents and scalling functions near the phase transition point stated in 4 are obtained for certain systems.

Report

(4 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1987 Annual Research Report
  • 1986 Annual Research Report
  • Research Products

    (74 results)

All Other

All Publications (74 results)

  • [Publications] Byon Chol So.: Physica D. 21. 126-136 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hazime Mori: Physica D. 21. 355-370 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: Progress of Theoretical Physics. 76. 752-767 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hazime Mori: Progress of Theoretical Physics. 76. 784-801 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: Progress of Theoretical Physics. 77. 239-253 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 森肇: 数理科学. 291号. 5-12 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Terumitsu Morita: Progress of Theoretical Physics. 78. 511-515 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroki Hata: Progress of Theoretical Physics. 78. 721-726 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: Progress of Theoretical Physics. 79. 1-6 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Terumitsu Morita: Progress of Theoretical Physics. 79. 296-312 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hisao Okamoto: Progress of Theoretical Physics. 79. 581-599 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Nobuyuki Mori: Progress of Theoretical Physics. 79. 1260-1264 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 吉田健: 数理科学. 301号. 68-74 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takehiko Horita: Progress of Theoretical Physics. 80. 793-808 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroki Hata: Progress of Theoretical Physics. 80. 809-826 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 岡本寿夫: 日本機械学会誌. 91. 11-16 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takehiko Horita: Progress of Theoretical Physics. 80. 923-928 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Koji Tomita: Progress of Theoretical Physics. 80. 953-972 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Koji Tomita: Progress of Theoretical Physics. 81. 1-6 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroki Hata: Progress of Theoretical Physics. 81. 11-16 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Nobuyuki Mori: Progress of Theoretical Physics. 81. 60-76 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Tatsuharu Kobayashi: Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Koji Tomita: Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takehiko Horita: Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 吉田健: 日本物理学会誌 4月号. 44. (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Syuji Miyazaki: Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Byon Chol So: "Asymptotic Shapes of Power Spectra of Intermittent Chaos near Its Onset Point" Physica D. 21. 126-136 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hazime Mori: "Spectral Structure of Intermittent Chaos" Physica D. 21. 355-370 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: "Characteristic Structures of Power Spectra in Periodic Chaos" Progress of Theoretical Physics. 76. 752-767 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hazime Mori: "Global Spectral Structures of Intermittent Chaos" Progress of Theoretical Physics. 76. 784-801 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: "Characteristic Structures of Power Spectra in Periodic Chaos. II. - The Henon Map, the Driven Damped Pendulum and the Rossler System -" Progress of Theoretical Physics. 77. 239-253 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hazime Mori: "Fractal - Its Recent Movement -" Surikagaku. No.291. 5-12 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Terumitsu Morita: "On Partial Dimensions and Spectra of Singularities of Strange Attractors" Progress of Theoretical Physics. 78. 511-515 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroki Hata: "Spectra of Singularities for Lozi and Henon Maps" Progress of Theoretical Physics. 78. 721-726 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: "Spectra of Singularities and Entropies for Local Expansion Rates" Progress of Theoretical Physics. 79. 1-6 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Terumitsu Morita: "Spatial and Temporal Scaling Properties of Strange Attractors and Their Representations by Unstable Periodic Orbits" Progress of Theoretical Physics. 79. 296-312 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hisao Okamoto: "Global Spectral Structures of Type III Intermittent Chaos" Progress of Theoretical Physics. 79. 581-599 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Nobuyuki Mori: "Power Spectra of Intermittent Chaos Due to the Collapse of Period-3 Windows" Progress of Theoretical Physics. 79. 1260-1264 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: "Structures of Chaos as Looked through Phase Transitions (in Japanese)" Surikagaku. No.301. 68-74 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takehiko Horita: "Local Structures of Chaotic Attractors and q-Phase Transitions at Attractor-Merging Crises in the Sine-Circle Maps" Progress of Theoretical Physics. 80. 793-808 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroki Hata: "Characterization of Local Structures of Chaotic Attractors in Terms of Coars-Grained Local Expansion Rates" Progress of Theoretical Physics. 80. 809-826 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takehiko Horita: "Singular Local Structures of Chaotic Attractors Due to Collisions with Unstable Periodic Orbits in Two-Dimensional Naps" Progress of Theoretical Physics. 80. 923-928 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Koji Tomita: "Scaling Structures of Chaotic Attractors and q-Phase Transitions at Crises in the Henon and the Annulus Maps" Progress of Theoretical Physics. 80. 953-972 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Koji Tomita: "Classification of Collisions of Chaotic Attractors with Unstable Periodic Orbits in Terms of the q-Phase Transitions" Progress of Theoretical Physics. 81. 1-6 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Hiroki Hata: "Singular Local Structures of Chaotic Attractors and q-Phase Transitions of Spatial Scaling Structures" Progress of Theoretical Physics. 81. 11-16 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Nobuyuki Mori: "Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos" Progress of Theoretical Physics. 81. 60-76 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Tatsuharu Kobayashi: "Critical Scaling Laws of Dynamic Structure Functions for Type I Intermittent Chaos" Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Koji Tomita: "q-Phase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points" Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takehiko Horita: "Dynamics of Critical Tori at the Onset of Chaos and Critical KAM Tori" Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Syuji Miyazaki: "q-Phase Transitions and Critical Phenomena near the Band Crisis Point of Chaotic Attractors" Progress of Theoretical Physics.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Takeshi Yoshida: "One-Dimensional Chaos and Symbolic Dynamics" BUTSURI. 44 No.4. (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 吉田健: 数理科学. 301号. 68-74 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Takehiko Horita.: Progress of Theoretical Physics. 80. 793-808 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Hiroki Hata.: Progress of Theoretical Physics. 80. 809-826 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Takehiko Horita.: Progress of Theoretical Physics. 80. 923-928 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Koji Tomita.: Progress of Theoretical Physics. 80. 953-972 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Koji Tomita.: Progress of Theoretical Physics. 81. 1-6 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] Hiroki Hata.: Progress of Theoretical Physics. 81. 11-16 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] Nobuyuki Mori.: Progress of Theoretical Physics. 81. 60-77 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] Tatsuharu Kobayashi.: Progress of Theoretical Physics.

    • Related Report
      1988 Annual Research Report
  • [Publications] Koji Tomita.: Progress of Theoretical Physics.

    • Related Report
      1988 Annual Research Report
  • [Publications] Takehiko Horita.: Progress of Theoretical Physics.

    • Related Report
      1988 Annual Research Report
  • [Publications] Syuji Miyazaki.: Progress of Theoretical Physics.

    • Related Report
      1988 Annual Research Report
  • [Publications] Takeshi Yoshida;Byon Chol So: Progress of Theorefical Physics. 79. 1-6 (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] Terumitsu Morita et al.: Progress of Theoretical Physics. 78. 511-515 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] Hiroshi Hata et al.: Progress of Theoretical Physics. 78. 721-726 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] Terumitsu Morita et al: Progress of Theorefical Physics. 79. 296-312 (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] Hisao Okamoto et al: Progress of Theoretical Physics. 79. No. 3 (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] 森肇: 数理科学. 291. 5-12 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] Takeshi Yoshida: Progress of Theoretical Physics. 76. 752-767 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Takeshi Yoshida: Progress of Theoretical Physics. 77. 239-253 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] Byon Chol So: Physica D. 21. 126-136 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Hazime Mori: Physica D. 21. 355-370 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Hazime Mori: Progress of Theoretical Physics. 76. 784-801 (1986)

    • Related Report
      1986 Annual Research Report

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Published: 1987-03-31   Modified: 2016-04-21  

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