Prog. Theor. Phys. Vol. 106 No. 5 (2001) pp. 909-915
Global Period-Doubling Bifurcation in the Standard Map
1College of Engineering, Chubu University, Kasugai 487-8501, Japan
2National Institute for Fusion Science, Toki 509-5292, Japan
(Received June 4, 2001)
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.
DOI : 10.1143/PTP.106.909
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Citing Article(s) :
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