| Original Articles |
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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
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| Cite this article: |
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ZHOU Ji-Lin, Bam-Bi HU, SUN Yi-Sui 2001 Chin. Phys. Lett. 18 734-736 |
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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.
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| Keywords:
05.45.-a
02.30.Hq
47.20.Ky
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Published: 01 June 2001
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| PACS: |
05.45.-a
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(Nonlinear dynamics and chaos)
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02.30.Hq
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(Ordinary differential equations)
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47.20.Ky
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(Nonlinearity, bifurcation, and symmetry breaking)
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