  We generalize the classical K\"onig's and B\"ottcher's Theorems in complex
dynamics to certain quasiregular mappings in the plane. Our approach to these
results is unified in the sense that it does not depend on the local
injectivity, or not, of the map at the fixed point. By passing to the
logarithmic transform we obtain a quasiconformal mapping in either case.
Certain restrictions on the quasiregular mappings are needed in order for there
to be a candidate to linearize to. These are provided by requiring a simple
infinitesimal space of the mapping at the fixed point and restricting to the
BIP mappings introduced by the authors in prior work.
