日時：2026/07/28(火) 15:00-16:00
場所：総合研究10号館317室
講演者：竹口佳輝
タイトル：ある1次元荷電三体問題の非可積分性とシンボリック計算による証明
アブストラクト：直線上の三つの質点が逆二乗力で相互作用する，一次元荷電三体問題（1-dimensional C3BP）を考える．Morales-Ramis理論に基づき，等質量の1次元荷電三体問題は有理型の第一積分をもつような，Liouvilleの意味での可積分系にはならないことを示す．一次元重力三体問題が任意の質量比に対して非可積分であることの別証明も与える．証明はシンボリック計算を利用する．
Date: From 3 p.m. to 4 p.m. Tuesday, July 28th 2026
Location: Room 317, Research Bldg. No. 10
Speaker: Yoshiki Takeguchi
Title: Non-integrability of some one-dimensional charged three-body problems and its proof via symbolic computation
Abstract: We consider the charged three-body problem in one dimension, where three point masses on a line interact via inverse-square forces. Based on Morales-Ramis theory, we prove that the charged three-body problem with equal masses is not integrable in the Liouville sense with meromorphic first integrals. We also give another proof of the non-integrability of the gravitational three-body problem in one dimension for arbitrary mass ratios. Our proofs rely on symbolic computation.