  We investigate the generation of fractional-period states in continuum
periodic systems. As an example, we consider a Bose-Einstein condensate
confined in an optical-lattice potential. We show that when the potential is
turned on non-adiabatically, the system explores a number of transient states
whose periodicity is a fraction of that of the lattice. We illustrate the
origin of fractional-period states analytically by treating them as resonant
states of a parametrically forced Duffing oscillator and discuss their
transient nature and potential observability.
