Author:
Pommerenke Christian,Toro Margarita
Abstract
We study various aspects of the family of groups generated by the parabolic matrices A(t1 ζ), ... , A(tm ζ) where A(z) = ( 1 z0 1 ) and by the elliptic matrix ( 0 -1 1 0 ). The elements of the matrices W in such groups can be computed by a recursion formula. These groups are special cases of the generalized parametrized modular groups introduced in [16].We study the sets {z : tr W(z) ∈ [-2; +2]} [13] and their critical points and geometry, furthermore some finite index subgroups and the discretness of subgroups.
Publisher
Universidad Nacional de Colombia
Reference21 articles.
1. A.F. Beardon, The geometry of discrete groups, Springer, New York, 1983.
2. N. Bircan and Ch. Pommerenke, On chebyshev polynomials and GL2; Z=pZ, Bull.Math.Soc.Sci.Math.Roumanie 55 (2012), 353-364.
3. P.M. Cohn, A presentation of SL2 for euclidean imaginary quadratic number fields, Mathematik 15 (1968), 156-163.
4. A. Eremenko and W.K. Hayman, On the length of lemniscates, Mich. Math.J. 46 (1999), no. 2, 409-415.
5. M. Fekete, Über den transfiniten durchmesser ebener punktmengen ii, Math.Z. 32 (1930), 215-221.