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We show that the breaking of the rotation symmetry of spiral waves intwo-dimensional complex (period-doubled or chaotic) oscillatory media bysynchronization defect lines (SDL) is accompanied by an intrinsic drift of thepattern. Single vortex motion changes from ballistic flights at a well-definedangle from the SDL to Brownian-like diffusion when the turbulent character ofthe medium increases. It gives rise, in non-turbulent multi-spiral regimes, toa novel ``vortex liquid''.Comment: 5 pages, 4 figure

From Ballistic to Brownian Vortex Motion in Complex Oscillatory Media