Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1973
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1973ap%26ss..25..373f&link_type=abstract
Astrophysics and Space Science, Volume 25, Issue 2, pp.373-386
Astronomy and Astrophysics
Astrophysics
12
Scientific paper
We continue to study the number of isolating integrals in dynamical systems with three and four degrees of freedom, using as models the measure preserving mappingsT already introduced in preceding papers (Froeschlé, 1973; Froeschlé and Scheidecker, 1973a). Thus, we use here a new numerical method which enables us to take as indicator of stochasticity the variation withn of the two (respectively three) largest eigenvalues-in absolute magnitude-of the linear tangential mappingT n * ofT n . This variation appears to be a very good tool for studying the diffusion process which occurs during the disappearance of the isolating integrals, already shown in a previous paper (Froeschlé, 1971). In the case of systems with three degrees of freedom, we define and give an estimation of the diffusion time, and show that the gambler's ruin model is an approximation of this diffusion process.
Froeschlé Ch.
Scheidecker J. P.
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