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Box-Counting Dimension and Beyond
Archer, Kassie
Archer, Kassie
Abstract
This paper explores different analytical and computational methods of computing the box-counting dimension of a fractal-like set, such as the attractor associated with a chaotic dynamical system. Because attractors cannot be described exactly, but can only be approximated by computational methods, the box-counting dimension is typically measured computationally. Using alternative measures of chaotic behavior, such as the Lyapunov exponents, it is possible to estimate the accuracy of a computational approximation. The box-counting dimension definition is extended to include subsets of regular subspaces of R?. These sets include products of Cantor sets and attractors associated with infinite dimensional dynamical systems, such as the Kot-Schaffer model. Computational approaches to computing the box-counting dimension of the Kot-Schaffer attractor are discussed and the results for this attractor are discussed.
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Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.
Date
2009-05-18
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Keywords
Lyapunov exponents, Box-counting dimension, Infinite dimensional dynamical systems
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Department
Mathematics