A numerical study of the stabilization effect of steepness |
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| Authors: | Nata?a Todorovi? Massimiliano Guzzo Elena Lega Claude Froeschlé |
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| Institution: | 1.Belgrade Astronomical Observatory,Belgrade,Serbia;2.Dipartimento di Matematica Pura ed Applicata,Padova,Italy;3.UNSA, UMR CNRS 6202 Cassiopée,Nice Cedex 4,France |
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| Abstract: | We present the results of numerical experiments about the influence of steepness on the resonant structure, stability and
diffusion in a 4-dimensional symplectic map. The map is designed so that by changing a parameter, we smoothly switch steepness
on and off by the change of the so called steepness coefficients. In both cases we measure the diffusion coefficients of the
actions within a resonance. According to Nekhoroshev theorem we find that, in the steep case, the diffusion coefficients are
definitely smaller than in the non steep one, thus confirming the threshold effect of the steepness coefficients which comes
from the proof of Nekhoroshev theorem. |
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