Abstract
For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set \({\mathcal{U}}\) in phase space of fixed measure, where the set of initial points which lead to collision is \({O(\mu^\frac{1}{20})}\) dense as \({\mu\rightarrow 0}\).
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The authors thank Alain Albouy, Alain Chenciner and Jacques Féjoz for helpful discussions and remarks on a preliminary version of the paper.
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This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 757802). M. G. has been also partially supported by the Spanish MINECO-FEDER Grant MTM2015-65715-P and the Catalan Grant 2017SGR1049. V.K. acknowledges partial support of the NSF Grant DMS-1402164. The three authors acknowledge the hospitality of the ETH Institute for Theoretical Studies and the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.
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Guardia, M., Kaloshin, V. & Zhang, J. Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem. Arch Rational Mech Anal 233, 799–836 (2019). https://doi.org/10.1007/s00205-019-01368-7
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DOI: https://doi.org/10.1007/s00205-019-01368-7