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Escape Time Weighting of Unstable Stationary Solutions of Spatiotemporal Chaos

Scott M. Zoldi
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Abstract

By computing 254 unstable stationary solutions of the Kuramoto-Sivashinsky equation in the extensive chaos regime (Lyapunov fractal dimension D=8.8), we find that 30% satisfy the symmetry of the time-average pattern of the spatiotemporal chaos. Using a symmetry pruning of unstable stationary solutions, the escape-time weighting average converges to the time-average pattern of the chaotic attractor as O(1/N), where N is the total number of unstable stationary solutions and unstable periodic orbits in the average.

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Scott M. Zoldi. 1999-03-17. Escape Time Weighting of Unstable Stationary Solutions of Spatiotemporal Chaos. https://arxiv.org/abs/chao-dyn/9903020

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