0000000000793954
AUTHOR
Jérôme Daquin
A New Analysis of the Three-Body Problem
In the recent papers [5, 18], respectively, the existence of motions where the perihelions afford periodic oscillations about certain equilibria and the onset of a topological horseshoe have been proved. Such results have been obtained using, as neighbouring integrable system, the so-called two-centre (or Euler) problem and a suitable canonical setting proposed in [16, 17]. Here we review such results.
Symbolic dynamics in a binary asteroid system
We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczy\'nski, combined with a recent analysis of an associated secular problem.