关于一类广义标准映射的KAM环面研究(英文)  

On the Study of KAM Tori in a Class of Generalized Standard Maps

作　　者：袁晓风 陈龙伟[2] 

机构地区：[1]中科院成都分院计算机所数理室,成都610041 [2]云南大学数学系,昆明650091

出　　处：《云南大学学报（自然科学版）》1998年第S2期291-296,共6页Journal of Yunnan University(Natural Sciences Edition)

摘　　要：研究了自函数Φ（ｘ）＝（１／２π）ｓｉｎ３２πｘ产生的广义标准映射，讨论了ＫＡＭ曲线的临界行为，按照Ｇｒｅｅｎ的方法，使用Ｑｉ环的序列去近似“黄金法”不变环，计算出了参数ｋ的临界值，还研究了在参数临界值ｋｃ处的标变律．Kolmogorov - Arnol'd - Moser curves are studied in a family of generalized standard maps in which the function Φ(x) = (1/2πx) sin32πx .The critical behavior of a KAM curves is analysed. Following Green,we use a series of Qi cycles to approximate the 'Golden - Mean' invariant circle.The critical value of parameter k has been computed.The scaling behavior at the critical point kc is also studied.

关 键 词：KAM曲线 辛映射 切空间 余数 

分 类 号：O175[理学—数学]