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Box-Counting Dimension and Beyond

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Author: Archer, Kassie
Advisor: Day, Sarah, 1975-
Committee Members: Lutzer, D. J. (David John), 1943-; Lewis, Robert Michael; Delos, John
Issued Date: 2009-05-18
Subjects: Lyapunov exponents
Box-counting dimension
Infinite dimensional dynamical systems
URI: http://hdl.handle.net/10288/1259
Description: 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.
Degree: Bachelors of Science in Mathematics


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