Golden torus

Figure 6. Variation with time of the FLI for a set of periodic orbits belonging to the Fibonacci sequence for the standard map with e = 0.9715. The rational ratios Pk/qk, k = 1,. ..7, are written in the figure near the corresponding FLI curve. The FLI curve which grows linearly with time all over the interval 0 < t < 5 106 iterations is obtained for the golden torus.

In Figure 6 the FLI curve which grows linearly with time all over the interval 0 < t < 5 106 iterations is obtained for the golden torus. 

Figure 7. FLI-map as a function of the logarithmic distance to the golden torus for the standard map with e = 0.9715 From top to bottom enlargement of the box of the previous figure analyzed on a longer time as indicated on each figure.

Davis and Gray also demonstrated the existence of a series of intramolecular energy transfer bottlenecks, each corresponding to the breakup of a KAM torus. For example, for I2 in the vibrational state v = 20 they found intramolecular bottlenecks associated with frequency ratios equal to (3 + g) and up. However, Davis and Gray found that the last golden mean torus to be broken up is the most effective bottleneck to intramolecular energy transfer and is therefore... 

Figure 4.20 Classical surface of section associated with the CS stretch normal mode of OCS showing the following regions (A) total energy contour, (B) 3 1 resonance islands, (C) 5 2 resonance islands, (D) outer boundary of quasi-periodic region, (E) golden mean torus between chaotic regions labeled I and II, (T) turnstile (in golden mean torus) between regions I and II (located by arrow) (Gibson et al., 1987).

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