Prog. Theor. Phys. Vol. 81 No. 6 (1989) pp. 1073-1078

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Letters

Dynamics on Critical Tori at the Onset of Chaos and Critical KAM Tori

Takehiko Horita, Hiroki Hata, Hazime Mori and Koji Tomita

Department of Physics, Kyushu University 33, Fukuoka 812

(Received December 26, 1988)

Abstract:

Motion on a critical invariant torus with the golden-mean rotation number is studied by the sum of the local expansion rates along the torus, S_n = ∑^n-1_i=0 λ₁(X_i). It is found that β_n = S_n/logn is recurrent for large n and its time series exhibits a remarkable self-similarity specified by the Fibonacci sequence.

URL : http://ptp.ipap.jp/link?PTP/81/1073/
DOI : 10.1143/PTP.81.1073

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Citing Article(s) :

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
Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 897-910 :
Dynamic Description of the Critical 2^∞ Attractor and 2^m-Band Chaos

Hiroki Hata, Takehiko Horita and Hazime Mori
Progress of Theoretical Physics Vol. 83 No. 5 (1990) pp. 829-834 :
Dynamic Scaling Laws for the Intermittent Switching between Two Bands

Hiroshi Shibata, Shoichi Kuroki and Hazime Mori
Progress of Theoretical Physics Vol. 84 No. 4 (1990) pp. 558-562 :
Cascade of Attractor-Merging Crises to the Critical Golden Torus and Universal Expansion-Rate Spectra

Takehiko Horita, Hiroki Hata and Hazime Mori
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
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
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