Parabolic solutions for the planar $N$-centre problem: multiplicity and scattering

Alberto Boscaggin, Walter Dambrosio, Duccio Papini

For the planar $N$-centre problem $$\ddot{x}=-\sum _{i=1}^N\frac{m_i(x-c_i)}{|x-c_i{|}^{\alpha +2}},x\in {\mathbb{R}}^2\setminus \{c_1,\dots ,c_N\},$$ where $m_i>0$ for…