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Contact geometry in the restricted three-body problem: a survey

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This survey is based on lecture notes for an online mini-course taught for postgraduate students at UDELAR, Montevideo, Uruguay, in November 2020, remotely from the Mittag–Leffler Institute in Djursholm, Sweden. Lectures were recorded and are available online.

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Notes

  1. In this section, we will use the symbol \(\vec {}\;\) for vectors in \({\mathbb {R}}^3\) to make our formulas for Moser regularization simpler. We will use the convention that \(\xi \in {\mathbb {R}}^4\) has the form \((\xi _0,\vec \xi )\).

  2. This was discussed at the opening lectures by Hofer and Floer in Fall 1988 at the symplectic program at the MSRI Berkeley, although unfortunately is written nowhere. Hofer gave a lecture on capacities and the \(S^1\)-equivariant symplectic homology at a conference in Durham in 1989, whose proceedings are published in [33], and contains the non-equivariant part of the story. I thank Hofer for these clarifications.

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Acknowledgements

The author wishes to thank all of those present (virtually and physically) during the lectures: Helmut Hofer (who also provided more accurate historical background), Chris Wendl (who also provided useful background, and corrected my pronunciation on Eastern-European names), Otto van Koert (who also provided amazing pictures and videos, and stayed up until 2am to watch the lectures), Urs Frauenfelder, Ezequiel Maderna, Paolo Ghiggini (Povero Paolo!), Alex Takeda, Jagna Wiśniewska, Fabio Gironella ...to name a few whom I remember seeing on the screen; sorry if I missed you, and thank you. I am also very grateful to my uruguayan colleagues Alejandro Passeggi and Rafael Potrie for hel** me organize this, to Gabriele Benedetti for pointing out a mathematical flaw in the work of the author with Otto van Koert, and to all the students in Uruguay, Sweden, and abroad (e.g., Turkey, France, US, South Korea, ...) who showed interest in the project. This material is based on work supported by the Swedish Research Council under Grant No. 2016-06596, while the author was in residence at Institut Mittag–Leffler in Djursholm, Sweden during the Winter Semester, 2020.

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    Agustin Moreno

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This article is part of the topical collection “Symplectic geometry—A Festschrift in honour of Claude Viterbo’s 60th birthday” edited by Helmut Hofer, Alberto Abbondandolo, Urs Frauenfelder, and Felix Schlenk.

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Moreno, A. Contact geometry in the restricted three-body problem: a survey. J. Fixed Point Theory Appl. 24, 29 (2022). https://doi.org/10.1007/s11784-022-00956-7

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