Abstract

Recently Bishop constructed the first example of a bounded-type transcendental entire function with a wandering domain using a new technique called quasiconfomal folding. It is easy to check that his method produces a function of infinite order. We construct the first examples of functions in the class $mathcal B$ of finite order with wandering domains. In Bishop's example, as well as in our construction, the wandering domains are of oscillating type, that is, with an unbounded non-escaping orbit. To build such function, we use quasiconformal interpolation instead of quasiconformal folding, which is much more straightforward. Our examples have order $p/2$ for any $pinmathbb{N}$ and thus, since functions in the class $mathcal B$ have order at least $1/2$, we can achieve the smallest possible order. This is a joint work with Mitsuhiro Shishikura.