Geodesic
Fractal theory of Saturn's ring
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 95-111

Voir la notice de l'article provenant de la source Math-Net.Ru

The true reason, in our opinion, for the partition of Saturn's ring as well as the rings of other planets into a large number of small subrings is found. This reason is clarified by the Zelikin–Lokutsievskiy–Hildebrand theorem about the fractal structure of solutions to generic piecewise smooth Hamiltonian systems. The instability of the two-dimensional model of the ring with continuous surface density of the distribution of particles is proved both for the Newton and Boltzmann equations. We do not claim that we have solved the problem of stability of Saturn's ring. We rather put questions and suggest some ideas and means for future research. 
@article{TRSPY_2015_291_a8,
     author = {M. I. Zelikin},
     title = {Fractal theory of {Saturn's} ring},
     journal = {Informatics and Automation},
     pages = {95--111},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a8/}
}
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M. I. Zelikin. Fractal theory of Saturn's ring. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 95-111. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a8/