Supercritical Behavior of Disordered Orbits of a Circle Map
Supercritical Behavior of Disordered Orbits of a Circle Map
复制标题
圆图无序轨道的超临界行为
DOI：
10.1143/ptp.72.1089
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发表时间：
1984
影响因子：
--
通讯作者：
K. Kaneko
中科院分区：
文献类型：
--
作者：
K. Kaneko
圆形映射的超临界行为xn+ l = xn+ a sin（2jz“ xn）+ d。窗户显示了参数空间中的相似性（a，d）。窗户宽度的关键现象由指数II代表给定的非理性旋转数的圆环的速度。接下来，引入了“无序”的概念，以表征混乱的轨道。 。它的缩放行为是附录中的研究。
Supercritical behavior of the circle map Xn+l =Xn+ A sin(2JZ"xn)+ D is investigated. The windows show the similarity in the parameter space (A, D). The critical phenomena of the width of the windows are characterized by the exponent II, which represents the speed of the collapse of a torus for a given irrational rotation number. Its value is well explained by the RG theory which was originally invented by Feigenbaum et al. and Rand et al. for the subcritical behavior. Next, the notion of "disordering" is introduced to characterize chaotic orbits. The distribution of disordering times is calculated with the use of the induced maps. The distribution shows an exponential decay. The ratio of the decay is related to the instability of unstable cycles. The scaling of the decay is also represented by the exponent II. A conjecture is proposed that the golden mean torus is the first KAM to collapse. Lastly, the period· adding sequence .near the crisis and its scaling behavior are studied in the Appendix.