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Prog. Theor. Phys. Vol. 78 No. 3 (1987) pp. 511-515

[ Full Text PDF : FREE ACCESS (227K) ]

Letters

On Partial Dimensions and Spectra of Singularities of Strange Attractors

Terumitsu Morita, Hiroki Hata, Hazime Mori, Takehiko Horita and Koji Tomita

Department of Physics, Kyushu University 33, Fukuoka 812

(Received May 6, 1987)

Abstract:

New relations of the generalized dimensions and entropies of strange attractors to the fluctuations of divergence rates of nearby orbits and to the eigenvalues of the Jacobian matrices of unstable periodic points are obtained in order to derive the sspectra of singularities from the dynamical viewpoints.


URL : http://ptp.ipap.jp/link?PTP/78/511/
DOI : 10.1143/PTP.78.511

[ Full Text PDF : FREE ACCESS (227K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 78 No. 4 (1987) pp. 721-726 :
    Spectra of Singularities for the Lozi and Hénon Maps
    Hiroki Hata, Terumitsu Morita, Koji Tomita and Hazime Mori
  2. Progress of Theoretical Physics Vol. 79 No. 1 (1988) pp. 1-6 :
    Spectra of Singularities and Entropies for Local Expansion Rates
    Takeshi Yoshida and Byon Chol So
  3. Progress of Theoretical Physics Vol. 79 No. 2 (1988) pp. 296-312 :
    Spatial and Temporal Scaling Properties of Strange Attractors and Their Representations by Unstable Periodic Orbits
    Terumitsu Morita, Hiroki Hata, Hazime Mori, Takehiko Horita and Koji Tomita
  4. Progress of Theoretical Physics Vol. 79 No. 3 (1988) pp. 581-599 :
    Global Spectral Structures of Type III Intermittent Chaos
    Hisao Okamoto, Hazime Mori and Shoichi Kuroki
  5. Progress of Theoretical Physics Vol. 80 No. 5 (1988) pp. 793-808 :
    Local Structures of Chaotic Attractors and q-Phase Transitions at Attractor-Merging Crises in the Sine-Circle Maps
    Takehiko Horita, Hiroki Hata, Hazime Mori, Terumitsu Morita, Koji Tomita, Shoichi Kuroki and Hisao Okamoto
  6. Progress of Theoretical Physics Vol. 80 No. 5 (1988) pp. 809-826 :
    Characterization of Local Structures of Chaotic Attractors in Terms of Coarse-Grained Local Expansion Rates
    Hiroki Hata, Takehiko Horita, Hazime Mori, Terumitsu Morita and Koji Tomita
  7. Progress of Theoretical Physics Vol. 80 No. 6 (1988) pp. 923-928 :
    Singular Local Structures of Chaotic Attractors Due to Collisions with Unstable Periodic Orbits in Two-Dimensional Maps
    Takehiko Horita, Hiroki Hata, Hazime Mori Terumitsu Morita and Koji Tomita
  8. Progress of Theoretical Physics Vol. 80 No. 6 (1988) pp. 953-972 :
    Scaling Structures of Chaotic Attractors and q-Phase Transitions at Crises in the Hénon and the Annulus Maps
    Koji Tomita, Hiroki Hata, Takehiko Horita, Hazime Mori and Terumitsu Morita
  9. Progress of Theoretical Physics Vol. 81 No. 1 (1989) pp. 1-6 :
    Classification of Collisions of Chaotic Attractors with Unstable Periodic Orbits in Terms of the q-Phase Transitions
    Koji Tomita, Hiroki Hata, Takehiko Horita, Hazime Mori and Terumitsu Morita
  10. Progress of Theoretical Physics Vol. 81 No. 1 (1989) pp. 11-16 :
    Singular Local Structures of Chaotic Attractors and q-Phase Transitions of Spatial Scaling Structures
    Hiroki Hata, Takehiko Horita, Hazime Mori, Terumitsu Morita and Koji Tomita
  11. Progress of Theoretical Physics Vol. 81 No. 1 (1989) pp. 60-77 :
    Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos
    Nobuyuki Mori, Tatsuharu Kobayashi, Hiroki Hata, Terumitsu Morita, Takehiko Horita and Hazime Mori
  12. Progress of Theoretical Physics Vol. 81 No. 6 (1989) pp. 1124-1134 :
    q-Phase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points
    Koji Tomita, Hiroki Hata, Takehiko Horita, Hazime Mori, Terumitsu Morita, Hisao Okamoto and Hirotaka Tominaga
  13. Progress of Theoretical Physics Vol. 82 No. 1 (1989) pp. 1-6 :
    Critical Scaling Laws of Dynamic Structure Functions for Type I Intermittent Chaos
    Tatsuharu Kobayashi, Nobuyuki Mori, Hiroki Hata, Tekehiko Horita, Takeshi Yoshida and Hazime Mori
  14. Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 879-896 :
    The q-Phase Transition and Critical Scaling Laws near the Band-Crisis Point of Chaotic Attractors
    Takeshi Yoshida, Syuji Miyazaki, Hazime Mori, Tatsuharu Kobayashi, Takehiko Horita and Hiroki Hata
  15. Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 897-910 :
    Dynamic Description of the Critical 2∞ Attractor and 2m-Band Chaos
    Hiroki Hata, Takehiko Horita and Hazime Mori
  16. Progress of Theoretical Physics Vol. 83 No. 4 (1990) pp. 649-654 :
    q-Phase Transitions and Dynamic Scaling Laws at Attractor-Merging Crises in the Driven Damped Pendulum
    Toru Murayama, Hirotaka Tominaga, Hazime Mori, Hiroki Hata and Takehiko Horita
  17. Progress of Theoretical Physics Vol. 84 No. 1 (1990) pp. 18-22 :
    Linearities of the f(α) Spectrum at Bifurcations of Chaos in Dissipative Differential Systems
    Hirotaka Tominaga, Hiroki Hata, Takehiko Horita, Hazime Mori and Koji Tomita
  18. Progress of Theoretical Physics Vol. 84 No. 4 (1990) pp. 553-557 :
    Dynamic Scaling Laws for Bifurcations of Chaos in Dissipative Differential Systems
    Hirotaka Tominaga, Takehiko Horita and Hazime Mori
  19. Progress of Theoretical Physics Vol. 86 No. 2 (1991) pp. 355-369 :
    Crossover of the f(α) Spectra between Critical and Chaotic Regime, and Universal Critical Scaling Laws for Two-Dimensional Fractality
    Hirotaka Tominaga and Hazime Mori
  20. Progress of Theoretical Physics Vol. 91 No. 6 (1994) pp. 1081-1100 :
    Hopf Bifurcations and Chaos in the S-Shaped I-V Characteristic Systems
    Hirotaka Tominaga and Hazime Mori
  21. Progress of Theoretical Physics Supplement No.99 (1989) pp. 1-63 :
    Statistical Mechanics of Dynamical Systems
    Hazime Mori, Hiroki Hata, Takehiko Horita and Tatsuharu Kobayashi
  22. Progress of Theoretical Physics Supplement No.99 (1989) pp. 64-81 :
    Global Bifurcations and Fluctuation Spectra of Local Expansion Rates in Nonlinear Dynamical Systems
    Takeshi Yoshida and Syuji Miyazaki
  23. Progress of Theoretical Physics Supplement No.99 (1989) pp. 82-94 :
    “Thermodynamics”, Temporal Correlations and Scaling Laws
    Hirokazu Fujisaka and Masayoshi Inoue

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