  A new general class of exact solutions is presented for the time evolution of
a bubble of arbitrary initial shape in a Hele-Shaw cell when surface tension
effects are neglected. These solutions are obtained by conformal mapping the
viscous flow domain to an annulus in an auxiliary complex-plane. It is then
demonstrated that the only stable fixed point (attractor) of the non-singular
bubble dynamics corresponds precisely to the selected pattern. This thus shows
that, contrary to the established theory, bubble selection in a Hele-Shaw cell
does not require surface tension. The solutions reported here significantly
extend previous results for a simply-connected geometry (finger) to a
doubly-connected one (bubble). We conjecture that the same selection rule
without surface tension holds for Hele-Shaw flows of arbitrary connectivity. We
also believe that this mechanism can be found in other, similarly described,
selection problems.
