Dr Katie Gittins katie.gittins@durham.ac.uk
Assistant Professor
Some spectral applications of McMullen's Hausdorff dimension algorithm
Gittins, K.; Peyerimhoff, N.; Stoiciu, M.; Wirosoetisno, D.
Authors
Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor
M. Stoiciu
Dr Djoko Wirosoetisno djoko.wirosoetisno@durham.ac.uk
Associate Professor
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 |
Files
Accepted Journal Article
(1.3 Mb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Statement
© 2012 American Mathematical Society. First published in Conformal geometry and dynamics volume 16 published by the American Mathematical Society.
You might also like
Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter
(2021)
Journal Article
Upper bounds for Courant-sharp Neumann and Robin eigenvalues
(2020)
Journal Article
Heat Flow from Polygons
(2020)
Journal Article
Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter
(2020)
Journal Article