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Wilkinson, M.; Mehlig, B.; Gustavsson, K. and Werner, E.
(2012).
DOI: https://doi.org/10.1140/epjb/e2011-20325-5
Abstract
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.
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About
- Item ORO ID
- 35495
- Item Type
- Journal Item
- ISSN
- 1434-6028
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2012 EDP Sciences
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- Depositing User
- Michael Wilkinson