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Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension
(Johns Hopkins University Press, 1998)
This paper presents an eigenvalue algorithm for accurately computing the Hausdorff dimension of limit sets of Kleinian groups and Julia sets of rational maps. The algorithm is applied to Schottky groups, quadratic polynomials ...
Self-Similarity of Siegel Disks and Hausdorff Dimension of Julia Sets
(Springer Netherlands, 1998)
Let f(z) = e2 i z +z2, where θ is an irrational number of bounded type. According
to Siegel, f is linearizable on a disk containing the origin. In this paper we show:
• the Hausdorff dimension of the Julia set J(f) is ...
Rigidity and Inflexibility in Conformal Dynamics
(Universität Bielefeld, Fakultät für Mathematik, 1998)
Elder Siblings and the Taming of Hyperbolic 3-Manifolds
(Academia Scientiarum Fennica, 1998)
A 3-manifold is tame if it is homeomorphic to the interior of a compact manifold with boundary. Marden’s conjecture asserts that any hyperbolic 3-manifold \(\mathbb{M} = \mathbb{H}^3/\Gamma\) with \(\pi_1(M)\) finitely-generated ...
Complex Earthquakes and Teichmuller Theory
(American Mathematical Society, 1998)
It is known that any two points in Teichmuller space are joined by an earthquake path. In this paper we show any earthquake path \(\mathbb{R} \rightarrow T(S)\) extends to a proper holomorphic mapping of a simplyconnected ...
Lipschitz Maps and Nets in Euclidean Space
(Springer Verlag, 1998)
Kleinian Groups and John Domains
(Elsevier, 1998)
We characterize when John domains arise in the setting of Kleinian
groups.