  The breakup of a jet of a viscous fluid with viscosity $\mu _{1}$ immersed
into another viscous fluid with viscosity $\mu _{2}$ is considered in the limit
when the viscosity ratio $\lambda =\mu _{1}/\mu _{2}$ is close to zero. We show
that, in this limit, a transition from ordinary continuous selfsimilarity to
discrete selfsimilarity takes place as $\lambda $decreases. The result being
that instead of a single point breakup, the rupture of the inner jet occurs
through the appearance of an infinite sequence of filaments of decreasing size
that will eventually produce infinite sequences of bubbles of the inner fluid
inside the outer fluid. The transition can be understood as the result of a
Hopf bifurcation in the system of equations modelling the physical problem.
