  We compute the semi-global symplectic invariants near the hyperbolic
equilibrium points of the Euler top. The Birkhoff normal form at the hyperbolic
point is computed using Lie series. The actions near the hyperbolic point are
found using Frobenius expansion of its Picard-Fuchs equation. We show that the
Birkhoff normal form can also be found by inverting the regular solution of the
Picard-Fuchs equation. Composition of the singular action integral with the
Birkhoff normal form gives the semi-global symplectic invariant. Finally, we
discuss the convergence of these invariants and show that in a neighbourhood of
the separatrix the pendulum is not symplectically equivalent to any Euler top.
