Some spectral applications of McMullen’s Hausdorff dimension algorithm

Gittins, K.; Peyerimhoff, N.; Stoiciu, M.; Wirosoetisno, D.

doi:10.1090/S1088-4173-2012-00244-5

Some spectral applications of McMullen’s Hausdorff dimension algorithm
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by K. Gittins, N. Peyerimhoff, M. Stoiciu and D. Wirosoetisno

Conform. Geom. Dyn. 16 (2012), 184-203

DOI: https://doi.org/10.1090/S1088-4173-2012-00244-5

Published electronically: July 25, 2012

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Abstract:

Using McMullen’s Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane. Varying these geodesics, we found four minima in the two-dimensional parameter space, leading to a rigorous result why this must be so. Extending the algorithm to compute the limit measure and its moments, we study orthogonal polynomials on the unit circle associated with this measure. Several numerical observations on certain coefficients related to these moments and on the zeros of the polynomials are discussed.

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