  We consider frequency fluctuations in self-sustained oscillators based on
nonlinear underdamped resonators. An important type of such resonators are
nano- and micro-electro-mechanical systems. Various noise sources are
considered, with the emphasis on the fundamentally unavoidable noise that comes
along with dissipation from the coupling to a thermal reservoir. The
formulation in terms of the action-angle variables of the resonator allows us
to study a deeply nonlinear regime. In this regime the vibration frequency as a
function of the action can have an extremum. We show that frequency
fluctuations can be strongly reduced by choosing the operation point at this
extremum. We suggest a practical implementation of a nanoresonator that has the
appropriate property and show explicit results for the corresponding model.
