| Abstract: |
| In this talk, we consider the spatial isosceles three body problem. For certain choices of energy and angular momentum, the dynamics on the energy surface is equivalent to a Reeb flow on the tight three-sphere. We find a Hopf link formed by the Euler orbit and a symmetric brake orbit, which spans an open book decomposition whose pages are annulus-like global surfaces of section. The convexity and non-convexity of the energy surface will also be discussed. Then we will adress the dynamical consequences of these facts, in particular the existence of periodic solutions. |
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