Wilkinson, M.; Mehlig , B.; Gustavsson, K. and Werner, E.
|DOI (Digital Object Identifier) Link:||http://doi.org/10.1140/epjb/e2011-20325-5|
|Google Scholar:||Look up in Google Scholar|
It might be expected that trajectories of a dynamical system which has no negative Lyapunov exponent (implying exponential growth of small separations) will not cluster together. However, clustering can occur such that the density ρ(Δx) of trajectories within distance |Δx| of a reference trajectory has a power-law divergence, so that ρ(Δx)~|Δx|−β when |Δx| is sufficiently small, for some 0 < β < 1. We demonstrate this effect using a random map in one dimension. We find no evidence for this effect in the chaotic logistic map, and argue that the effect is harder to observe in deterministic maps.
|Item Type:||Journal Article|
|Copyright Holders:||2012 EDP Sciences|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
|Depositing User:||Michael Wilkinson|
|Date Deposited:||21 Nov 2012 15:42|
|Last Modified:||18 Jan 2016 16:04|
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