  We have measured the dynamics of individual magnetic fluxoids entering and
leaving photolithographically patterned thin film rings of the underdoped
high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, using a
variable sample temperature scanning SQUID microscope. These results can be
qualitatively described using a model in which the fluxoid number changes by
thermally activated nucleation of a Pearl vortex in, and transport of the Pearl
vortex across, the ring wall.
