  We give a statistical characterization of states with nonzero winding number
in the Phase Turbulence (PT) regime of the one-dimensional Complex
Ginzburg-Landau equation. We find that states with winding number larger than a
critical one are unstable, in the sense that they decay to states with smaller
winding number. The transition from Phase to Defect Turbulence is interpreted
as an ergodicity breaking transition which occurs when the range of stable
winding numbers vanishes. Asymptotically stable states which are not
spatio-temporally chaotic are described within the PT regime of nonzero winding
number.
