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Universal Behaviour on the Break-up of the Spiral Mean Torus
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| ZHOU Ji-Lin1;Bambi HU2;SUN Yi-Sui1 |
| 1Department of Astronomy and Center of Astronomy and
Astrophysics in Eastern China, Nanjing University, Nanjing 210093
2Department of Physics and Center for Nonlinear Studies, Hong Kong Baptist University, Hong Kong
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| Cite this article: |
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ZHOU Ji-Lin, Bambi HU, SUN Yi-Sui 2001 Chin. Phys. Lett. 18 1550-1553 |
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Abstract 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 paramter 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 are revealed on the possible existence of a univsersal 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.
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| Keywords:
05.45.+b
02.30.Hq
47.20.Ky
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Published: 01 December 2001
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