Examples of heteroclinic connections. Dots are the stroboscopic projection of fluid trajectories to $ϕ0=0$⁠. The blue lines in each figure represent an initially small circle about the hyperbolic point P [or P₁ in (c)] being advected and shown after 42 (a), 6 (b), and 20 (c) periods of lid motion. Lines in cyan represent an initially small circle about the point Q [or P₂ in (c)] advected backward in time. In (a), stable and unstable manifolds are indicated by green and red arrows, respectively. Black, gray, and magenta colors as in Fig. 7. (a) Str = 0.05, Re = 5, (b) Str = 0.02, Re = 10, and (c) Str = 0.25, Re = 50.