  We study the internal dynamics of multiply connected wandering domains of
meromorphic functions. We do so by considering the sequence of injectivity
radii along the orbit of a base point, together with the hyperbolic distortions
along the same orbit. The latter sequence had been previously used in this
context; the former introduces geometric information about the shape of the
wandering domains that interacts with the dynamic information given by the
hyperbolic distortions. Using this idea, we complete the description of the
internal dynamics of any wandering domain of a meromorphic function, and also
unify previous approaches to the question. We conclude that the internal
dynamics of a wandering domain, from the point of view of hyperbolic geometry,
can be classified into six different types. Five of these types are realised by
wandering domains of entire functions, while the sixth can only arise for
meromorphic functions: a locally but not globally eventually isometric
wandering domain. We construct a meromorphic function with such a domain,
demonstrating that this new phenomenon does in fact occur. Our results show
that, on a local level, the dynamics of multiply connected wandering domains of
meromorphic functions is similar to those of entire functions, although new
global phenomena can arise for non-entire functions.
