A Continuous, Nowhere-Differentiable Function with a Dense Set of Proper Local Extrema
Description:
In this paper, we use the following scheme to construct a continuous, nowhere-differentiable function π which is the uniform limit of a sequence of sawtooth functions πβ : [0, 1] β [0, 1] with increasingly sharp teeth. Let π = [0, 1] x [0, 1] and πΉ(π) be the Hausdorff metric space determined by π. We define contraction maps π€β , π€β , π€β on π. These maps define a contraction map π€ on πΉ(π) via π€(π΄) = π€β(π΄) β π€β(π΄) β π€β(π΄). The iteration under π€ of the diagonal in π defines a sequence of graphs ofβ¦
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Date:
December 1993
Creator:
Huggins, Mark C. (Mark Christopher)
Partner:
UNT Libraries