| Abstract: |
| The restricted planar circular 3-body problem (RPC3BP) has a critical point called $L_3$, which is a saddle-center. If the ratio between the mass of the primaries is small, the hyperbolic eigenvalues are larger than the elliptic ones.
In this talk, we present the first steps towards the computation of the distance between the stable and unstable manifolds of $L_3$, which is exponentially small (and therefore, classical perturbative methods do not apply).
We approximate the model by an average integrable system and analyze its complex singularities. Moreover, we derive and analyze the so-called inner equation associated to this problem, which is a good approximation of the original system on a suitable neighborhood of the complex singularities.
This inner equation gives the leading term of the distance between the stable and unstable manifolds of $L_3$. |
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