Estimate of the Transition Value of Librational Invariant Curves |
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| Authors: | Alessandra Celletti Gabriella Della Penna Claude Froeschlé |
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| Institution: | (1) Dipt. di Matematica, Universitá di Roma 'Tor Vergata', Via della Ricerca Scientifica, I-00133 Roma, Italy;(2) Observatoire de Nice, BP 229, F-06304 Nice Cedex 4, France |
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| Abstract: | We investigate the break-down threshold of librational invariant curves. As a model problem, we consider a variant of a mapping introduced by M. Hénon, which well describes the dynamics of librational motions surrounding a stable invariant point. We verify in concrete examples the applicability of Greene's method, by computing the instability transition values of a sequence of periodic orbits approaching an invariant curve with fixed noble frequency. However, this method requires the knowledge of the location of the periodic orbits within a very good approximation. This task appears to be difficult to realize for a libration regime, due to the different topology of the phase space. To compute the break-down threshold, we tried an alternative method very easy to implement, based on the computation of the fast Lyapunov indicators and frequency analysis. Such technique does not require the knowledge of the periodic orbits, but again, it appears very difficult to have a precision better than Greene's method for the computation of the critical parameter. |
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| Keywords: | librational curves break-down threshold fast Lyapunov indicators Hé non's mapping |
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