Infinitely Many Eclipses
动力系统
2007-05-23 v1 微分几何
摘要
We show that any bounded zero-angular momentum solution for the Newtonian three-body problem must suffer infinitely many eclipses, or collinearities, provided that it does not suffer a triple collision. Motivation for the result comes from the dream of building a symbolic dynamics for the three-body problem, one whose symbols 1, 2, 3 representing the three types of eclipses. The proof involves the conformal geometry of the shape sphere.
关键词
引用
@article{arxiv.math/0110300,
title = {Infinitely Many Eclipses},
author = {Richard Montgomery},
journal= {arXiv preprint arXiv:math/0110300},
year = {2007}
}
备注
14 pages. See also http://www.count.ucsc.edu/~rmont