  Blowing up a point p in a manifold M builds a new manifold M' in which p is
replaced by the projectivization of the tangent space of M at p. This
well-known operation also applies to fixed points of diffeomorphisms, yielding
continuous homomorphisms between automorphism groups of M and M'. The
construction for maps involves a loss of regularity and is not unique at the
lowest order of differentiability. Fixed point sets and other aspects of
blownup dynamics at the singular locus are described in terms of derivative
data; continuous data are not sufficient to determine much about these issues.
