[1]曾令宏,陈媛媛,周济林.双频标准映射不变环面的破裂[J].南京师大学报(自然科学版),2010,33(04):39-43.
　Zeng Linghong,Chen Yuanyuan,Zhou Jilin.Breakup of Last KAM Torus in Double-Frequency Standard Map[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(04):39-43.
点击复制

双频标准映射不变环面的破裂()
分享到：

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第33卷
期数:
2010年04期
页码:
39-43
栏目:
物理学
出版日期:
2010-12-20

文章信息/Info

Title:
Breakup of Last KAM Torus in Double-Frequency Standard Map
作者:
曾令宏1;  陈媛媛2;  周济林2
1. 柳州师范高等专科学校, 广西柳州545004 2. 南京大学天文系, 江苏南京210093
Author(s):
Zeng Linghong1; Chen Yuanyuan2; Zhou Jilin2
1.Liuzhou Teachers College,Liuzhou 545004,China 2. D epartm en t of Astronom y, Nan jing U n ivers ity, Nan jing 210093, Ch ina
关键词:
保守系统;  KAM 环面;  临界现象;  轨道扩散
Keywords:
conserva tive sy stem s;  KAM tor; i critical phenom enon;  o rbita l diffusion
分类号:
O19
摘要:
利用旋转数方法以及周期轨道方法确定了双频标准映射中最后一个不变环面破裂的频率为(73+13(51/2))/(309+55 (51/2)),属于黄金分割频率族,其在连分数展开下具有[4,4,3,3,1,…,1,…]的形式.该环面破裂的临界摄动参数约为0.4476.与单频标准映射相比,增加激发频率可以导致最后一个环面的临界摄动参数减小,使得系统的全局不稳定性增加,一些轨道更容易扩散到相空间作用量较大的地方.
Abstract:
The last KAM to rus in the doub le- frequency standard m ap under perturbation is inv estig ated w ith the m ethods o f rotation number and per iodic orb its. It has frequency ( 73 + 13 5) / ( 309 + 55 5 ), wh ich belongs to the Go lden m ean g roup, and has the form of [ 4, 4, 3, 3, 1, ,, 1, , ] under continuation fac tion expansion. The critical perturbation param eter is roughly 01 447 6 fo r th is to r.i As com pared w ith the last KAM torus in the standard m ap, the add itional exc itation frequency decreases the cr itica l perturba tion param eter, wh ich increases the instab ility of the system, thus som e orbits can be eas ier to d iffuse away in the phase space.

参考文献/References:

[ 1] 孙义燧, 周济林. 现代天体力学导论[M ]. 北京: 高等教育出版社, 2008.
[ 2] G reene JM. A m ethod for dete rm ining a stochastic transition[ J]. Journa l o fM a them a tics and Physics, 1979, 20( 6): 1 183- 1 201.
[ 3] 孙义燧, Froeschl?C. 二维保面积映射的Ko lmog rov熵[ J] . 中国科学, 1982, 25( 4): 357-363.
[ 4] Froeschle C, Guzzo M, Lega E. G raph ica l evo lu tion o f the A rno ld w eb: from order to chao s[ J]. Sc ience, 2000, 289 ( 5487) : 2 108-2 110.
[ 5] Zhou J L, H u B, Sun Y S. Break-up o f three- frequency KAM to r:i dete rm ina tion of the critica l param eters[ J]. Ch inese Physics Letter, 2001, 18( 6) : 734-736.
[ 6] Zhou J L, H u B, Sun Y S. Un iversial behav iour on the breakup o f the spiralm ean to rus[ J]. Chinese Phy sics Le tter, 2001, 18( 12) : 1 550-1 553.
[ 7] Liu J, Sun Y S. Chao tic mo tions of com ets in near-pa rabo lic o rbits: m apping approaches[ J]. C elestia lM echan ics and Dynam ica l Astronom y, 1994, 60( 1): 3-28.
[ 8] Pey rardM, Augry S. Cr itical behav iour at teh transition by breaking of ana ly tic ity in the discrete Frenke-lKontorova model [ J] . Journa l of Phys ics C: So lid State Physics, 1983, 16( 9): 1 593-1 608.
[ 9] Kook H, M eiss J D. Applica tion o f New ton. s m ethod to Lag rang ian m appings[ J] . Phys ica D, 1989, 36( 3): 317-326.

备注/Memo

备注/Memo:
基金项目: 国家科技部“973”计划(2007CB814800);国家自然科学基金(10833001);教育部博士点基金(20090091110002) 通讯联系人: 曾令宏, 副教授, 研究方向: 应用物理与非线性物理. E-mail:ZLH8188@163. com
更新日期/Last Update: 2013-04-08