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Prog. Theor. Phys. Vol. 106 No. 5 (2001) pp. 909-915

[ Full Text PDF : FREE ACCESS (1146K) ]

Global Period-Doubling Bifurcation in the Standard Map

Chieko Murakami,1 Wakako Murakami,1 Kei-ichi Hirose2 and Yoshi H. Ichikawa1

1College of Engineering, Chubu University, Kasugai 487-8501, Japan
2National Institute for Fusion Science, Toki 509-5292, Japan

(Received June 4, 2001)

Abstract:

While there has been great effort to establish universal behavior of the sequence of period-doubling bifurcation in Hamiltonian systems with few degrees of freedom, the nature of the period-doubling bifurcation is far more complicated in two-dimensional maps. Though the onset of instability is determined by a local, linear property of the system, the area of a bifurcated region in the phase space increases gradually when the control parameter increases beyond the critical threshold. Scaling laws for the growth process of the period-doubling bifurcation are elucidated for the period-2 step-1 accelerator mode and for the fundamental fixed orbit in the standard map.


URL : http://ptp.ipap.jp/link?PTP/106/909/
DOI : 10.1143/PTP.106.909

[ Full Text PDF : FREE ACCESS (1146K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 108 No. 4 (2002) pp. 669-678 :
    Dynamical Ordering of Periodic Accelerator Modes in the Standard Mapping
    Yoshihiro Yamaguchi and Kiyotaka Tanikawa

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