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arXiv · 1602.02897

Scattering parabolic solutions for the spatial N-centre problem

Alberto Boscaggin·Walter Dambrosio·Susanna Terracini
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Abstract

For the $N$-centre problem in the three dimensional space, $$ \ddot x = -\sum_{i=1}^{N} \frac{m_i \,(x-c_i)}{\vert x - c_i \vert^{α+2}}, \qquad x \in \mathbb{R}^3 \setminus \{c_1,\ldots,c_N\}, $$ where $N \geq 2$, $m_i > 0$ and $α\in [1,2)$, we prove the existence of entire parabolic trajectories having prescribed asymptotic directions. The proof relies on a variational argument of min-max type. Morse index estimates and regularization techniques are used in order to rule out the possible occurrence of collisions.

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Alberto Boscaggin, Walter Dambrosio, Susanna Terracini. 2016-02-09. Scattering parabolic solutions for the spatial N-centre problem. https://doi.org/10.1007/s00205-016-1057-0

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