The open problem
Study the Thue-Morse trace map; in particular, find the asymptotics of the Hausdorff dimension of the spectrum as the coupling constant tends to zero or infinity.
• We studied the dynamics of the Thue-Morse trace map.
• We developed MATLAB code to help approximate the box-counting dimension, thickness, and Hausdorff measure of the Schrödinger operator with Thue-Morse potential.
• We analysed the resulting data, which confirmed conjectures about the asymptotic behavior of the fractal dimensions of the operator. Asymptotic Spectral Properties of the Schr¨odinger Operator with Thue-
Clark, William; Kline, Rachael; and Stone, Michaela, "Asymptotic Spectral Properties of the Schrödinger Operator With Thue-Morse Potential" (2014). Undergraduate External Publications. Paper 4.
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