Errata for “Cubic polynomial maps with periodic critical orbit, Part II: Escape regions”

In this note we fill in some essential details which were missing from our paper. In the case of an escape region E h \mathcal {E}_h with non-trivial kneading sequence, we prove that the canonical parameter t t can be expressed as a holomorphic function of the local parameter η = a − 1 / μ \eta =a^{-1/\mu } (where a a is the periodic critical point). Furthermore, we prove that for any escape region E h \mathcal {E}_h of grid period n ≥ 2 n\ge 2 , the winding number ν \nu of E h \mathcal {E}_h over the t t -plane is greater or equal than the multiplicity μ \mu of E h \mathcal {E}_h .