The n-tree approximation scheme, introduced in the context of random directed polymers, is applied here to the computation of the maximum Lyapunov exponent in a coupled-map lattice. We discuss both an exact implementation for small tree depth n and a numerical implementation for larger n. 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.
|Number of pages||6|
|Journal||Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - Nov 1997|
- DIRECTED POLYMERS
- 1/D EXPANSION