via Saldini 50, 20133 Milano, Italy
Dipartimento di Matematica Universita degli Studi di Milano
Locatelli U., Giorgilli A.
Construction of Kolmogorov's normal form for a planetary system
2005, vol. 10, no. 2, pp. 153-171
We describe an algorithm constructing an invariant KAM torus for a class of planetary systems, such that the mutual attractions, the eccentricities and the inclinations of the planets are small enough. By using computer algebra, we explicitly implement this algorithm for approximating a KAM torus for the problem of three bodies in a case similar to the Sun–Jupiter–Saturn system. We show that, by reducing the masses of the planets by a factor 10 and with a small displacement of the orbits, our semianalytical construction of the torus turns out to be successful.
Giorgilli A., Lazutkin V. F., Simó C.
Visualization of a Hyperbolic Structure in Area Preserving Maps
1997, vol. 2, nos. 3-4, pp. 47-61
We present a simple method which displays a hyperbolic structure in the phase space of an area preserving map. The method is illustrated for the case of the Carleson standard map. As it follows from our experiments, the structure of the chaotic zone for the standard map is different from the one found for the systems of Anosov type.