  In the paper 'On the dynamics of polynomial-like mappings' Douady and Hubbard
introduced the notion of polynomial-like maps. They used it to identify
homeomophic copies of the Mandelbrot set inside the Mandelbrot set. They
conjectured that in case of primitive copies the homeomorphism between the
homeomorphic copy of the Mandelbrot set and the Mandelbrot set is q.-c., and
similarly in the satellite case, it is q.-c. off any small neighborhood of the
root. These conjectures are now Theorems due to Lyubich. The satellite copies
of the Mandelbrot set are clearly not q-c homeomorphic to the Mandelbrot set.
But are they mutually q-c homeomorphic? Or even q-c homeomorphic to half of the
logistic Mandelbrot set? In this paper we prove that, in general, the induced
Douady-Hubbard homeomorphism is not the restriction of a q-c homeomorphism: For
any two satellite copies of the Mandelbrot set, the induced Douady-Hubbard
homeomorphism is not q-c, if the root multipliers, which are primitive q and q'
roots of unity, have q different from q'.
