Prog. Theor. Phys. Vol. 84 No. 4 (1990) pp. 558-562

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Letters

Cascade of Attractor-Merging Crises to the Critical Golden Torus and Universal Expansion-Rate Spectra

Takehiko Horita, Hiroki Hata^* and Hazime Mori^**

Department of Physics, Kyushu University 33, Fukuoka 812
^*Department of Physics, Kagoshima University, Kagoshima 890
^**Faculty of Engineering, Kyushu Kyoritsu University, Kitakyushu 807

(Received May 25, 1990)

Abstract:

Two chaotic attractors with rotation number ρ_m=F_m-1/F_m, F_m being the m-th Fibonacci number, and ρ_m+1 just before their attractor-merging crisis converge to the critical golden torus as m→∞. A critical scaling is shown to hold for those chaotic attractors for large m, leading to a universal spectrum of the local expansion rates of nearby orbits.

URL : http://ptp.ipap.jp/link?PTP/84/558/
DOI : 10.1143/PTP.84.558

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Citing Article(s) :

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
Progress of Theoretical Physics Vol. 102 No. 6 (1999) pp. 1057-1064 :
Stochastic Resonance-Like Behavior in the Sine-Circle Map

Takehiko Horita, Takashi Kanamaru and Toru Akishita
Progress of Theoretical Physics Vol. 108 No. 2 (2002) pp. 231-240 :
Non-Birkhoff Periodic Orbits in a Circle Map

Yoshihiro Yamaguchi and Kiyotaka Tanikawa