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Some spectral applications of McMullen's Hausdorff dimension algorithm

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

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Authors

M. Stoiciu



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. - See more at: http://www.ams.org/journals/ecgd/2012-16-10/S1088-4173-2012-00244-5/home.html#sthash.MXrRFUVZ.dpuf

Citation

Gittins, K., Peyerimhoff, N., Stoiciu, M., & Wirosoetisno, D. (2012). Some spectral applications of McMullen's Hausdorff dimension algorithm. Conformal Geometry and Dynamics, 16, 184-203. https://doi.org/10.1090/s1088-4173-2012-00244-5

Journal Article Type Article
Online Publication Date Jul 25, 2012
Publication Date Jul 25, 2012
Deposit Date May 4, 2012
Publicly Available Date Sep 13, 2017
Journal Conformal Geometry and Dynamics
Print ISSN 1088-4173
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 16
Pages 184-203
DOI https://doi.org/10.1090/s1088-4173-2012-00244-5

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