  A family of three-dimensional travelling waves for flow through a pipe of
circular cross section is identified. The travelling waves are dominated by
pairs of downstream vortices and streaks. They originate in saddle-node
bifurcations at Reynolds numbers as low as 1250. All states are immediately
unstable. Their dynamical significance is that they provide a skeleton for the
formation of a chaotic saddle that can explain the intermittent transition to
turbulence and the sensitive dependence on initial conditions in this shear
flow.
