Break-Up of Three-Frequency KAM Tori: Determination of the
Critical Parameters
ZHOU Ji-Lin1, Bam-Bi HU2,3, SUN Yi-Sui1
1Department of Astronomy and Centre of Astronomy and Astrophysics in Eastern China, Nanjing University, Nanjing 210093
2Department of Physics and Centre for Nonlinear Studies, Hong Kong Baptist University, Hong Kong
3Department of Physics, University of Houston, Houston TX 77204 USA
Break-Up of Three-Frequency KAM Tori: Determination of the
Critical Parameters
ZHOU Ji-Lin1;Bam-Bi HU2,3;SUN Yi-Sui1
1Department of Astronomy and Centre of Astronomy and Astrophysics in Eastern China, Nanjing University, Nanjing 210093
2Department of Physics and Centre for Nonlinear Studies, Hong Kong Baptist University, Hong Kong
3Department of Physics, University of Houston, Houston TX 77204 USA
Abstract： 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.
(Nonlinearity, bifurcation, and symmetry breaking)
引用本文:
ZHOU Ji-Lin;Bam-Bi HU;SUN Yi-Sui. Break-Up of Three-Frequency KAM Tori: Determination of the
Critical Parameters[J]. 中国物理快报, 2001, 18(6): 734-736.
ZHOU Ji-Lin, Bam-Bi HU, SUN Yi-Sui. Break-Up of Three-Frequency KAM Tori: Determination of the
Critical Parameters. Chin. Phys. Lett., 2001, 18(6): 734-736.
2001, Vol. 18 
