Finite size Lyapunov exponent at a saddle point

A simple stochastic system is considered modeling Lagrangian motion in a vicinity of a hyperbolic stationary point in two dimensions. We address the dependence of the Finite Size Lyapunov Exponent (FSLE) λ on the diffusivity D and the direction of the initial separation θ. It is shown that there is an insignificant difference between the curves λ=λ(θ) for pure dynamics (D=0) and for infinitely large noise (D=∞). For small D a well known boundary layer asymptotic is employed and compared with numerical results.