InterJournal Complex Systems, 129
Status: Accepted
Manuscript Number: [129]
Submission Date: 971015
Generic mechanisms for hierarchies
Author(s): Didier Sornette

Subject(s): CX.08, CX.01

Category: Brief Article


Common to essentially all complex systems is the existence of a hierarchical organization, with transfers across the different levels from the smallest to the largest ones and vice-versa. Here, we propose that hierarchies are generically formed dynamically due to a spontaneous breakdown of continuous scale invariance into discrete scale invariance. We present a short introduction to the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. Proposed illustrations are diffusion-limited-aggregation clusters, rupture in heterogeneous systems, earthquakes, animals (a generalization of percolation) among several other systems. We refer to several papers and a recent review for further information, especially on the use for predictions.

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