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The structural stability of holomorphic functions has been the subject ofmuch research in the last fifty years. Due to various technicalities, however,most of that work has focused on so-called finite-type functions, implying thatfunctions with wandering domains - another hot topic of research in complexdynamics - have (for the most part) not been addressed in this context. Givenan entire function $f$ with a simply connected wandering domain $U$, weconstruct an object called a distortion sequence that, under some hypotheses,moves analytically as $f$ moves within appropriate parameter families. In orderto "ground" our discussion, we consider -- given an entire function $f$ -- theset $M_f$ of entire functions quasiconformally equivalent to $f$. Generalisingearlier results for the finite-type case, we show that if $f$ has a discreteset of singular values then $M_f$ admits the structure of a complex manifold(of possibly infinite dimension).

Parameter spaces and distortion sequences of entire functions with wandering domains