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Some spectral applications of McMullen's Hausdorff dimension algorithm.

Gittins, K. and Peyerimhoff, N. and Stoiciu, M. and Wirosoetisno, D. (2012) 'Some spectral applications of McMullen's Hausdorff dimension algorithm.', Conformal geometry and dynamics., 16 . pp. 184-203.

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

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1090/S1088-4173-2012-00244-5
Publisher statement:© 2012 American Mathematical Society. First published in Conformal geometry and dynamics volume 16 published by the American Mathematical Society.
Date accepted:No date available
Date deposited:13 September 2017
Date of first online publication:25 July 2012
Date first made open access:No date available

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