  Experiments and simulations lend mounting evidence for the edge state
hypothesis on subcritical transition to turbulence, which asserts that simple
states of fluid motion mediate between laminar and turbulent shear flow as
their stable manifolds separate the two in state space. In this Letter we
describe a flow homoclinic to a time-periodic edge state. Its existence
explains turbulent bursting through the classical Smale-Birkhoff theorem.
During a burst, vortical structures and the associated energy dissipation are
highly localized near the wall, in contrast to the familiar regeneration cycle.
