2020 Ian Snook Prize Problem : Three Routes to the Information Dimensions for One-Dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps

The $1000 Ian Snook Prize for 2020 will be awarded to the author(s) of the most interesting paper exploring pairs of relatively simple, but fractal, models of nonequilibrium systems, dissipative time-reversible Baker Maps and their equivalent stochastic random walks. Two-dimensional deterministic, time-reversible, chaotic, fractal, and dissipative Baker maps are equivalent to stochastic one-dimensional random walks. Three distinct estimates for the information dimension, {0.7897, 0.7415, 0.7337} have all been put forward for one such model. So far there is no cogent explanation for the differences among these estimates. We describe the three routes to the information dimension, DI : 1) iterated Cantor-like mappings, 2) mesh-based analyses of single-point iterations, and 3) the Kaplan-Yorke Lyapunov dimension, thought by many to be exact for these models. We encourage colleagues to address this Prize Problem by suggesting, testing, and analyzing mechanisms underlying these differing results.

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Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).