$1000 SNOOK PRIZES FOR 2021: The Information Dimensions of a Two-Dimensional Baker Map
Hoover William G. *, Hoover Carol G.
Ruby Valley Research Institute
601 Highway Contract 60
Ruby Valley, Nevada 89833, USA
*E-mail: hooverwilliam@yahoo.com
Received:
Received: 27 June 2021; in final form: 29 June 2021; published online: 30 June 2021
DOI: 10.12921/cmst.2021.0000021
Abstract:
The fractal information dimension can be computed in three ways: (1) mapping points, (2) mapping regions (two-dimensional areas here), and (3) applying the Kaplan-Yorke conjecture. For the simplest nonequilibrium Baker N2 Map these three approaches can give different results. A pedagogical exploration and explanation of this situation is the 2021 Ian Snook Prize Problem.
Key words:
differential equations, fractals, maps, molecular dynamics, Snook Prizes
References:
[1] W.G. Hoover, C.G. Hoover, 2020 Ian Snook Prize Problem: Three Routes to the Information Dimensions for One-Dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps, Computational Methods in Science and Technology 25, 153–159 (2019).
[2] W.G. Hoover, C.G. Hoover, Nonequilibrium Molecular Dynamics, Fractal Phase-Space Distributions, the Cantor Set, and Puzzles Involving Information Dimensions for Two Compressible Baker Maps, Regular and Chaotic Dynamics 25, 412–423 (2020).
The fractal information dimension can be computed in three ways: (1) mapping points, (2) mapping regions (two-dimensional areas here), and (3) applying the Kaplan-Yorke conjecture. For the simplest nonequilibrium Baker N2 Map these three approaches can give different results. A pedagogical exploration and explanation of this situation is the 2021 Ian Snook Prize Problem.
Key words:
differential equations, fractals, maps, molecular dynamics, Snook Prizes
References:
[1] W.G. Hoover, C.G. Hoover, 2020 Ian Snook Prize Problem: Three Routes to the Information Dimensions for One-Dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps, Computational Methods in Science and Technology 25, 153–159 (2019).
[2] W.G. Hoover, C.G. Hoover, Nonequilibrium Molecular Dynamics, Fractal Phase-Space Distributions, the Cantor Set, and Puzzles Involving Information Dimensions for Two Compressible Baker Maps, Regular and Chaotic Dynamics 25, 412–423 (2020).
