### Abstract

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.

Original language | English |
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Pages (from-to) | 4998-5003 |

Number of pages | 6 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 56 |

Issue number | 5 |

Publication status | Published - Nov 1997 |

### Keywords

- DIRECTED POLYMERS
- 1/D EXPANSION
- CHAOS
- SYSTEMS