Date Thesis Awarded

5-2009

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Sarah Day

Committee Member

D. J. Lutzer

Committee Member

Robert Michael Lewis

Committee Member

John Delos

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.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

Comments

Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.

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