A new analysis of the three--body problem

2022/09/07 by Daquin, Jerome, Di Ruzza, Sara, Pinzari, Gabriella
#34C20 #37J10 #37J15 #37J40 #70F10 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2209.03114

Abstract

In the recent papers~[18],~[5], 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 \it Euler) problem and a suitable canonical setting proposed in~[16],~[17]. Here we review such results.

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