The class of solvable many-body problems "of goldfish type" is extended byincluding (the additional presence of) three-body forces. The solvable $N$-bodyproblems thereby identified are characterized by Newtonian equations of motionfeaturing 19 arbitrary "coupling constants". Restrictions on these constantsare identified which cause these systems - or appropriate variants of them - tobe isochronous or asymptotically isochronous, i.e. all their solutions to beperiodic with a fixed period (independent of the initial data) or to have thisproperty up to contributions vanishing exponentially as $t\rightarrow\infty$.
展开▼
机译：通过包括（附加存在的）三体力，扩展了“金鱼型”可解决的多体问题的类别。由此确定的可解决的$ N $-身体问题的特征在于具有19个任意“耦合常数”的牛顿运动方程。确定了对这些常数的限制，这些限制会导致这些系统（或其适当的变体）是等时的或渐近等时的，即，它们对具有固定周期（独立于初始数据）的非周期性的所有解，或者直到收益的该性质成指数地消失为$ t \ rightarrow \ infty $。
展开▼
