| Abstract: |
| Consider the planar three body problem with masses $m_0>0$, $m_1>0$, $m_2>0$, and assume that all three are not equal. We consider a Poincar\`{e} map defined on a section of the phase space. After reduction of the problem by its first integrals this is a $4$-dimensional map. We construct a hyperbolic invariant set of the Poincar\`{e} map where its dynamics is conjugated to the (infinite symbols) Bernouilli shift. As a consequence we prove the existence of chaotic motions and positive topological entropy for the planar three body problem. The chaotic behaviour also provides the existence of oscillatory motions for the planar three body problem. |
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