Se p 19 98 N - tree approximation for the Largest Lyapunov Exponent of a Coupled map lattice

The n-tree approximation scheme, introduced in the context of random directed polymers, is here applied to the computation of the maximum Lya-punov exponent in a coupled map lattice. We discuss both an exact implementation for small tree-depth n and a numerical implementation for larger ns. We find that the phase-transition predicted by the mean field approach shifts towards larger values of the coupling parameter when the depth n is increased. We conjecture that the transition eventually disappears.