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In this note we fill in some essential details which were missing from our paper. In the case of an escape region $ \mathcal{E}_h$ can be expressed as a holomorphic function of the local parameter $ \eta=a^{-1/\mu}$ is the periodic critical point). Furthermore, we prove that for any escape region $ \mathcal{E}_h$, the winding number $ \nu$ $ \mathcal{E}_h$-plane is greater or equal than the multiplicity $ \mu$ $ \mathcal{E}_h$ [ABSTRACT FROM AUTHOR]

The parameter space $ \mathcal{S}_p$ is a smooth affine algebraic curve whose genus increases rapidly with $ p$ $ \mathcal{S}_p$ $ \mathcal{S}_p$ $ \mathcal{S}_p$ [ABSTRACT FROM AUTHOR]