关于$n$ -体型问题广义解的奇性
On the singularities of generalized solutions to $n$--body type problems
摘要：
对一类具有奇异力的动力系统，包括具有牛顿势、拟齐次势和对数势的经典$N$ -体问题，建立了碰撞解的Sundman型渐近估计的有效性.解是指广义莫尔斯意义上的（局部-在空间和时间-最小轨迹相对于compensated支持的变化）和它们的统一限制。分析包括冯蔡佩尔定理的推广和碰撞孤立性的证明。此外，这样的渐近分析，以证明没有碰撞的局部最小轨迹。
英文摘要：
The validity of Sundman-type asymptotic estimates for collision solutions is established for a wide class of dynamical systems with singular forces, including the classical $N$--body problems with Newtonian, quasi--homogeneous and logarithmic potentials. The solutions are meant in the generalized sense of Morse (locally --in space and time-- minimal trajectories with respect to compactly supported variations) and their uniform limits. The analysis includes the extension of the Von Zeipel's Theorem and the proof of isolatedness of collisions. Furthermore, such asymptotic analysis is applied to prove the absence of collisions for locally minimal trajectories.
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