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题目： The two Levi-Civita regularizations

报告人：Alain ALBOUY教授（巴黎天文台）

摘要：Levi-Civita published in 1916, and republished in 1920 and 1924, a proof that the flow of the 3-dimensional 3-body problem may be regularized, that is, replaced by a smooth flow which passes the binary collisions without experiencing any kind of singularity. This proof is reproduced by Siegel in his book (1956). But from 1965, all the authors on the reg- ularization of the binary collisions considered that Levi-Civita only did the 2-dimensional case, and that the 3-dimensional case was first proposed in 1964 by Kustaanheimo, who extended in a sophisticated way the 2-dimensional regularization that Levi-Civita used in 1906. This is extremely surprising. What is then the status of Levi-Civita’s result in 1916? He claimed to regularize the flow, without any hypothesis on the value of the energy. If we replace his second regularization by the Kustaanheimo-Stiefel regularization, we cannot regularize the binary collisions with zero energy. If we replace it by Moser’s regularization (1970), which indeed Moser relates to Levi-Civita’s second regularization (see [2] p. 615), we have the same problem. I will propose a very simple improvement of Levi-Civita’s second regularization which confirms his argument. The improved regularization is still simpler than the KS regularization. 

报告时间：2025年5月27日（周二）上午10:30-11:30

报告地点：教二楼727

联系人：孙善忠