With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approac...With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approach the irrational winding number of the KAM torus,are examined.The break-up of quadratic frequency tori is characterized as the exponential growth of the residue means of the convergent periodic orbits.Critical parameters of the break-up of tori with different winding numbers are calculated,which shows that the spiral mean torus is the most robust one in our model.展开更多
基金Supported by Hong Kong Baptist University Faculty Research Grants,Hong Kong Grant Council Grantsthe National Natural Science Foundation of China under Grant Nos.19903001 and 19633010the Special Funds for Major State Basic Research Projects.
文摘With a four-dimensional symplectic map we study numerically the break-up of three-frequency Kolmogorov-Arnold-Moser(KAM)tori.The locations and stabilities of a sequence of periodic orbits,whose winding numbers approach the irrational winding number of the KAM torus,are examined.The break-up of quadratic frequency tori is characterized as the exponential growth of the residue means of the convergent periodic orbits.Critical parameters of the break-up of tori with different winding numbers are calculated,which shows that the spiral mean torus is the most robust one in our model.
