Author(s): Benedikt Remlein and Massimiliano Esposito Hopf bifurcations are a universal route to self-sustained oscillations in driven systems. Despite the absence of any singular stationary state, we show that time-averaged observables generically exhibit singularities at the onset of oscillations. The origin of this behavior is geometric: phase avera… [Phys. Rev. Lett. 137, 177101] Published Mon Oct 19, 2026