## Some spectral applications of McMullen’s Hausdorff dimension algorithm

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- by K. Gittins, N. Peyerimhoff, M. Stoiciu and D. Wirosoetisno PDF
- Conform. Geom. Dyn.
**16**(2012), 184-203 Request permission

## 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.## References

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## Additional Information

**K. Gittins**- Affiliation: Mathematical Sciences, Durham University, Mountjoy Site, South Road, Durham DH1 3LE, United Kingdom
- Email: katie.gittins@durham.ac.uk
**N. Peyerimhoff**- Affiliation: Mathematical Sciences, Durham University, Mountjoy Site, South Road, Durham DH1 3LE, United Kingdom
- MR Author ID: 290247
- Email: norbert.peyerimhoff@durham.ac.uk
**M. Stoiciu**- Affiliation: Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267
- Email: mstoiciu@williams.edu
**D. Wirosoetisno**- Affiliation: Mathematical Sciences, Durham University, Mountjoy Site, South Road, Durham DH1 3LE, United Kingdom
- Email: djoko.wirosoetisno@durham.ac.uk
- Received by editor(s): January 13, 2012
- Published electronically: July 25, 2012
- Additional Notes: The first author was supported by a Nuffield Undergraduate Research Bursary.
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**16**(2012), 184-203 - MSC (2010): Primary 37F35; Secondary 37F30, 42C05, 51M10, 58J50
- DOI: https://doi.org/10.1090/S1088-4173-2012-00244-5
- MathSciNet review: 2950130