We describe the statistical properties of growth rates of a linear oscillator driven by a parametric noise. We show that in general the fluctuations of local Lyapunov exponents are non-Gaussian and demonstrate multiscaling. Analytical calculations of the generalized Lyapunov exponents are complemented with approximative and numerical results; this allows us to identify the parameter range where the deviations from the Gaussian statistics become important.

• Received 10 March 2003

DOI:https://doi.org/10.1103/PhysRevE.67.061117