Persistent stability of a chaotic system

Huber, Greg; Pradas, Marc; Pumir, Alain and Wilkinson, Michael (2018). Persistent stability of a chaotic system. Physica A: Statistical Mechanics and its Applications, 492 pp. 517–523.

DOI: https://doi.org/10.1016/j.physa.2017.10.042

Abstract

We report that trajectories of a one-dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time, despite the fact that the system is chaotic. We provide a detailed quantitative description of this effect by developing the large-deviation theory for fluctuations of the finite-time Lyapunov exponent of this system. Specifically, the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods. The system has generic instability properties, and we consider the broader implications of our observation of long-term stability in chaotic systems.

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