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The authors construct a periodic quasiregular function of any finite order p, 1 < p < infinity. This completes earlier work of O. Martio and U. Srebro.

For an entire function $f$ let $N\left(z\right)=z-f\left(z\right)/f^{\prime }\left(z\right)$ be the Newton function associated to $f$. Each zero $\xi$ of $f$ is an attractive fixed point of $N$ and is contained in an invariant component of the Fatou set of the meromorphic function $N$ in which the iterates of $N$ converge to $\xi$. If $f$ has an asymptotic representation $f\left(z\right)\sim exp(-z^n),n\in \mathbb{N}$, in a sector $|argz|\<\epsilon$, then there exists an invariant component of the Fatou set where the iterates of $N$ tend to infinity. Such a component is called an invariant Baker domain. A question in the opposite...