Title
Centraliser of Analytic maps of parabolic type
Abstract
The local Analytic Centraliser near a fixed point is a simple problem in the case that it is attracting, repelling or Siegel due to local linearization. However in the cases of Cremer and Parabolic there is no local linearisation. Using parabolic renormalisation, I investigate the local Analytic centraliser of functions near a parabolic fixed point. Applying this approach specifically to the maps e^{2\pi i\frac{p}{q}}z+z^2, I show that the centraliser is trivial near 0.