Displaying similar documents to “Quasiconformal groups of compact type.”

Quasiconformal mappings of Y-pieces.

Christopher J. Bishop (2002)

Revista Matemática Iberoamericana

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In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.

Quasiconformal dimensions of self-similar fractals.

Jeremy T. Tyson, Jang-Mei Wu (2006)

Revista Matemática Iberoamericana

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The Sierpinski gasket and other self-similar fractal subsets of R, d ≥ 2, can be mapped by quasiconformal self-maps of R onto sets of Hausdorff dimension arbitrarily close to one. In R we construct explicit mappings. In R, d ≥ 3, the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have...

Non-rectifiable limit sets of dimension one.

Christopher J. Bishop (2002)

Revista Matemática Iberoamericana

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We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' beta's, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability...

Meromorphic functions of the form f(z) = Σ a/(z - z).

James Langley, John Rossi (2004)

Revista Matemática Iberoamericana

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We prove some results on the zeros of functions of the form f(z) = Σ a/(z - z), using quasiconformal surgery, Fourier series methods, and Baernstein's spread theorem. Our results have applications to fixpoints of entire functions.

Computation of centralizers in Braid groups and Garside groups.

Nuno Franco, Juan González-Meneses (2003)

Revista Matemática Iberoamericana

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We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers. ...