Masters Thesis

Box Counting Zeta Functions of Self-Similar Sets

In the first chapter we define and look at examples of self-similar sets and some of their properties. In the second chapter we introduce the theory of fractal strings and talk about various objects pertaining to them such as the geometric zeta func- tion, complex dimensions, and geometric counting function. We also briefly discuss Minkowski dimension and measurability. In chapter three we first define and work with examples of box counting functions. We then construct box counting fractal strings and examine some of their properties. The chapter ends with the introduc- tion of box counting content and measurability. Chapter four uses ideas from [3] to examine the structure of the box counting functions of some self-similar sets and then uses this structure to find a formula for their box counting zeta functions.

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