@inproceedings{0a9c4bf5d8b94134bb282778177f5ece,
title = "A New Analysis of the Three-Body Problem",
abstract = "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.",
keywords = "Chaos, Perihelion librations, Renormalizable integrability, Three-body problem, Two-centers problem",
author = "J{\'e}r{\^o}me Daquin and {Di Ruzza}, Sara and Gabriella Pinzari",
note = "Funding Information: Fig. 3 Composite panels illustrating our main steps in constructing the topological horseshoe. (Top left) The continuous flow is reduced to a 2-dimensional mapping by introducing a suitable Poincar{\'e} map P. The phase space contains both elliptic (blue) and hyperbolic (red) fixed-points. (Top right) Finite pieces of the stable and unstable manifolds might be constructed from the knowledge of the eigensystem derived from the linearisation DP. (Bottom) Carefully chosen sets and their images under P provide the covering relations and imply existence of symbolic dynamics. See text for details Acknowledgements The authors acknowledge the European Research Council (Grant 677793 Stable and Chaotic Motions in the Planetary Problem) for supporting them during the completion of the results described in the paper; warmly thank the organisers of I-CELMECH Training School that held in Milan in winter 2020 for their interest and especially U. Locatelli for a highlighting discussion. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; I-CELMECH Training School, 2020 ; Conference date: 03-02-2020 Through 07-02-2020",
year = "2022",
doi = "10.1007/978-3-031-13115-8_2",
language = "English",
isbn = "9783031131141",
volume = "399 ",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "47--79",
editor = "Giulio Ba{\`u} and {Di Ruzza}, Sara and P{\'a}ez, {Roc{\'i}o Isabel} and Tiziano Penati and Marco Sansottera",
booktitle = "New Frontiers of Celestial Mechanics",
}