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A fluid droplet suspended in an extensional flow of moderate intensity maybreak into pieces, depending on the amplitude of the initial dropletdeformation. In subcritical uniaxial extensional flow the non-breaking basestate is linearly stable, implying that only a finite amplitude perturbationcan trigger break-up. Consequently, the stable base solution is surrounded byits finite basin of attraction. The basin boundary, which separates initialdroplet shapes returning to the non-breaking base state from those becomingunstable and breaking up, is characterized using edge tracking techniques. Wenumerically construct the edge state, a dynamically unstable equilibrium whosestable manifold forms the basin boundary. The edge state equilibrium controlsif the droplet breaks and selects a unique path towards break-up. This pathphysically corresponds to the well-known end-pinching mechanism. Our resultsthereby rationalize the dynamics observed experimentally [Stone & Leal, J.Fluid Mech. 206, 223 (1989)]

Edge states control droplet break-up in sub-critical extensional flows