### Abstract

We investigate the structure of the invariant measure of space-time chaos by adopting an "open-system'' point of view. We consider large but finite windows of formally infinite one-dimensional lattices and quantify the effect of the interaction with the outer region by mapping the problem on the dynamical characterization of localized perturbations. This latter task is performed by suitably generalizing the concept of Lyapunov spectrum to cope with perturbations that propagate outside the region under investigation. As a result, we are able to introduce a "volume''-propagation velocity, i.e., the velocity with which ensembles of localized perturbations tend to fill volumes in the neighbouring regions.

Original language | English |
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Pages (from-to) | 205-228 |

Number of pages | 24 |

Journal | Journal of Statistical Physics |

Volume | 114 |

Issue number | 1-2 |

Publication status | Published - Jan 2004 |

### Keywords

- high-dimensional chaos
- fractals
- coupled map lattices
- numerical simulations of chaotic models
- COUPLED MAP LATTICES
- CHRONOTOPIC LYAPUNOV ANALYSIS
- STRANGE ATTRACTORS
- DYNAMICAL-SYSTEMS
- FRACTAL DIMENSION
- EXPONENTS
- EQUATION
- LIMIT

### Cite this

*Journal of Statistical Physics*,

*114*(1-2), 205-228.