  In shear flows at transitional Reynolds numbers, localized patches of
turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et
al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized
relative periodic solutions for pipe flow, which appeared in a saddle-node
bifurcation at low speeds. Combining slicing methods for continuous symmetry
reduction with Poincar\'e sections for the first time in a shear flow setting,
we compute and visualize the unstable manifold of the lower-branch solution and
show that it contains a heteroclinic connection to the upper branch solution.
Surprisingly this connection even persists far above the bifurcation point and
appears to mediate puff generation, providing a dynamical understanding of this
phenomenon.
