On Bifurcating Periodic Solutions at Low Frequency

A study is made of differential equations which have low‐frequency periodic bifurcating solutions. It is shown that the classical Poincaré‐Hopf technique for constructing periodic solutions encounters difficulties in the low‐frequency limit, and that the branches are determined by nonlinear, rather than linear, balances. Two types of models are investigated: one is autonomous and the other non‐autonomous, with a forcing term of small, fixed frequency. The latter model is relevant to several fluid‐dynamical situations.