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Computing fractal dimension in supertransient systems directly, fast and reliable

Romulus Breban·Helena E. Nusse
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Abstract

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by the presence of chaotic saddles whose stable sets have fractal dimensions that are close to phase-space dimension. For many physical systems chaotic saddles have a big impact on laboratory measurements, and it is important to compute the dimension of such stable sets including fractal basin boundaries through a direct method. In this work, we present a new method to compute the dimension of stable sets of chaotic saddles directly, fast, and reliable.

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Romulus Breban, Helena E. Nusse. 2006-08-07. Computing fractal dimension in supertransient systems directly, fast and reliable. https://doi.org/10.1209/epl%2Fi2006-10407-y

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