Dynamics of Piecewise Continuous Functions
Siddiqui, Sauleh Ahmad
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In our paper, we explore the chaotic behavior of a class of piecewise continuous functions defined on an interval X in the real line. A function or curve is piecewise continuous if it is continuous at all but a finite number of points and the left and right hand side limits exist at those points. In particular we will be looking at the piecewise continuous function for which the pieces are affine. We will show that show that f is locally eventually onto, has dense periodic points, and has sensitive dependence on initial conditions. We also show that f is quasiconjugate to a shift map of finite type to prove that f is chaotic. While functions such as f are known to be chaotic through proofs developed by measure theory, our paper is unique in that we use topological dynamics to show f is chaotic. Future work may extend these results to other compact metric spaces and more general piecewise continuous functions.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2007
- F&M Theses Collection