  We consider escape from a metastable state of a nonlinear oscillator driven
close to triple its eigenfrequency. The oscillator can have three stable states
of period-3 vibrations and a zero-amplitude state. Because of the symmetry of
period-tripling, the zero-amplitude state remains stable as the driving
increases. However, it becomes shallow in the sense that the rate of escape
from this state exponentially increases, while the system still lacks detailed
balance. We find the escape rate and show how it scales with the parameters of
the oscillator and the driving. The results facilitate using nanomechanical,
Josephson-junction based, and other mesoscopic vibrational systems for
studying, in a well-controlled setting, the rates of rare events in systems
lacking detailed balance. They also describe how fluctuations spontaneously
break the time-translation symmetry of a driven oscillator.
