# Clustering of exponentially separating trajectories - Nonlinear Sciences > Chaotic Dynamics

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Abstract: It might be expected that trajectories for a dynamical system which has nonegative Lyapunov exponent implying exponential growth of small separationswill not cluster together. However, clustering can occur such that the density$ho\Delta x$ of trajectories within distance $\Delta x$ of a referencetrajectory has a power-law divergence, so that $ho\Delta x\sim \Deltax^{-\beta}$ when $\Delta x$ is sufficiently small, for some $0<\beta<1$. Wedemonstrate this effect using a random map in one dimension. We find noevidence for this effect in the chaotic logistic map, and argue that the effectis harder to observe in deterministic maps.

Autor: M. Wilkinson, B. Mehlig, K. Gustavsson, E. Werner

Fuente: https://arxiv.org/