WINDING NUMBER INSTABILITY IN THE PHASE-TURBULENCE REGIME OF THE COMPLEX GINZBURG-LANDAU EQUATION

We give a statistical characterization of states with nonzero winding number in the phase turbulence (PT) regime of the one-dimensional comp lex Ginzburg-Landau equation. We find that states with winding numbers larger than critical ones are unstable in the sense that they decay t o states with smaller winding numbers. The transition from phase to de fect turbulence is interpreted as;an ergodicity breaking transition wh ich occurs when the range of stable winding numbers vanishes. Asymptot ically stable states which are not spatiotemporally chaotic are descri bed within the PT regime of a nonzero winding number.