Exponential localization of singular vectors in spatiotemporal chaos.

In a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval tau . We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law tau(-gamma) for the localization of the SV. Moreover the same exponent gamma characterizes the finite- tau deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improve existing forecasting techniques.