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2020 Ian Snook Prize Problem : Three Routes to the Information\n Dimensions for a One-Dimensional Stochastic Random Walk and for an Equivalent\n Prototypical Two-Dimensional Baker Map

2019/10/24 by William G. Hoover, Hoover, William Graham, Carol G. Hoover +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum chaos and dynamical systems #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1910.12642

openalex publication_date 2019/10/24 · openalex created_date 2022/09/15 · openalex updated_date 2026/07/28

Abstract

The \$1000 Ian Snook Prize for 2020 will be awarded to the author(s) of the\nmost interesting paper exploring a pair of relatively simple, but fractal,\nmodels of nonequilibrium systems, a dissipative time-reversible Baker Map and\nan equivalent stochastic random walk. The two-dimensional deterministic,\ntime-reversible, chaotic, fractal, and dissipative Baker map is equivalent to\nthe stochastic one-dimensional random walk model for which three distinct\nestimates for the information dimension, 0.7897, 0.7415, 0.7337 \nhave all been put forward. So far there is no cogent explanation for the\ndifferences among them. We describe the three routes to the information\ndimension, DI: [ 1 ] iterated Cantor-like mappings, [ 2 ] mesh-based\nanalyses of single-point iterations, and [ 3 ] the Kaplan-Yorke Lyapunov\ndimension, thought by many to be exact for these models. We encourage\ncolleagues to address this Prize Problem by suggesting, testing, and analyzing\nmechanisms underlying these differing results.\n

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