HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 80 (1988) > Number 6
| Next Article >

Prog. Theor. Phys. Vol. 80 No. 6 (1988) pp. 923-928

[ Full Text PDF : FREE ACCESS (324K) ]

Letters

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

Deparatment of Physics, Kyushu University 33, Fukuoka 812

(Received April 25, 1988)

Abstract:

The q-phase transition and the scaling exponent α of a singular local structure due to a collision with an unstable periodic orbit are formulated in terms of the eigenvalues of certain periodic orbits by taking into account the tangency of the chaotic attractor with the stable manifold of the periodic orbit.


URL : http://ptp.ipap.jp/link?PTP/80/923/
DOI : 10.1143/PTP.80.923

[ Full Text PDF : FREE ACCESS (324K) ] Citation:

References:

  1. P. Grassberger, Phys. Lett. 97A (1983), 227.
    H. G. E. Hentshel and I. Procaccia, Physica 8D (1983), 435[Elsevier].
  2. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procacia and B. I. Shraiman, Phys. Rev. A33 (1986), 1141[APS].
  3. T. Morita, H. Hata, H. Mori, T. Horita and K. Tomita, Prog. Theor. Phys. 78 (1987), 511[PTP]; ibid. 79 (1988), 296 [PTP]
    H. Hata, T. Morita, K. Tomita and H. Mori, Prog. Theor. Phys. 78 (1987), 721[PTP].
  4. R. Badii and A. Politi, Phys. Rev. A35 (1987), 1288[APS].
  5. T. Yoshida and B. C. So, Prog. Theor. Phys. 79 (1988), 1[PTP].
  6. P. Grassberger, R. Badii and A. Politi, J. Stat. Phys. 51 (1988), 135.
  7. H. Hata, T. Horita, H. Mori, T. Morita and K. Tomita, Prog. Theor. Phys. 80 (1988), 809[PTP].
  8. T. Horita, H. Hata, H. Mori, T. Morita, K. Tomita, S. Kuroki and H. Okamoto, Prog. Theor. Phys. 80 (1988), 793[PTP].
  9. K. Tomita, H. Hata, T. Horita, H. Mori and T. Morita, Prog. Theor. Phys. 80 (1988), 953[PTP].
  10. C. Grabogi, E. Ott and J. A. Yorke, Physica 7D (1983), 181[Elsevier].
  11. C. Grabogi, E. Ott, F. Romeiras and J. A. Yorke, Phys. Rev. A36 (1987), 5365, [APS]and references cited therein.
  12. H. Fujisaka, Prog. Theor. Phys. 70 (1983), 1264[PTP]; ibid. 71 (1984), 513[PTP].
  13. O. Lanford, in Statistical Mechanics and Mathematical Problems, ed. A. Lenard (Springer, New York, 1976).
    R. S. Ellis, Entropy, Large Deviations, and Statistical Mechanics (Springer-Verlag, New York, 1985).
  14. J. -P. Eckmann and I. Procaccia, Phys. Rev. A34 (1986), 659[APS].
    M. Sano, S. Sato and Y. Sawada, Prog. Theor. Phys. 76 (1986), 945[PTP].
    G. Paladin, L. Peliti and A. Vulpiani, J. of Phys. A19 (1986), L991[IoP STACKS].
  15. T. Bohr and D. Rand, Physica 25D (1987), 387[Elsevier].
  16. H. Fujisaka and M. Inoue, Prog. Theor. Phys. 77 (1987), 1334[PTP].

Citing Article(s) :

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. Progress of Theoretical Physics Vol. 91 No. 4 (1994) pp. 677-692 :
    On the Linear Slopes in the Expansion-Rate Spectra of Chaos
    Takehiko Horita and Hazime Mori
  11. 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
  12. 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

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.