Lyapunov exponents of poisson shot-noise velocity fields

Abstract

We consider the Lyapunov exponents of flows generated by a class of Markovian velocity fields. The existence of the exponents is obtained for Rows on a compact set, but with the most general form of the velocity field. As a particular class, we study the homogeneous and incompressible Rows. In this case, the exponents are nonrandom, free of the: initial position of the particle path, and their sum is zero. We numerically compute the top Lyapunov exponent on R(2) for a range of parameters to conjecture that it is strictly positive.