Universal Behaviour on the Break-up of the Spiral Mean Torus

作     者：ZHOU Ji-Lin Bambi HU SUN Yi-Sui 周济林;胡斑比;孙义燧

作者机构：Department of Astronomy and Center of Astronomy and Astrophysics in Eastern ChinaNanjing UniversityNanjing 210093 Department of Physics and Center for Nonlinear StudiesHong Kong Baptist UniversityHong Kong 

出 版 物：《Chinese Physics Letters》 (中国物理快报（英文版）)

年 卷 期：2001年第18卷第12期

页      面：1550-1553页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the National Natural Science Foundation of China under Grant No.19903001 the Special Funds for Major State Basic Research Projects,and Hong Kong Research Grant Council 

主　　题：indices critical periodic 

摘      要：We study numerically the critical behaviour during the break-up of the spiral mean torus in a four-dimensional symplectic map. At each point of the parameter space, the stability indices of a serial of periodic orbits are calculated with their winding numbers approaching the spiral mean torus. The critical values of the parameters when the torus breaks are determined by the criterion that the variance of the distribution on the indices reaches a minimum. Some evidence is revealed about the possible existence of a universal distribution on the stability indices of the periodic orbits at the critical This confirms the picture given by the approximate renormalization theory of the Hamiltonian systems with three degrees of freedom.