  Non-trivial topological behavior appears in many different contexts in
statistical physics, perhaps the most known one being the Kosterlitz-Thouless
phase transition in the two dimensional XY model. We study the behavior of a
simpler, one dimensional, XY chain with periodic boundary and strong
interactions; but rather than concentrating on the equilibrium measure we try
to understand its dynamics. The equivalent of the Kosterlitz-Thouless
transition in this one dimensional case happens when the interaction strength
scales like the size of the system $N$, yet we show that a sharp transition for
the dynamics occurs at the scale of $\log N$ -- when the interactions are
weaker than a certain threshold topological phases could not be observed over
long times, while for interactions that are stronger than that threshold
topological phases become metastable, surviving for diverging time scales.
