Kodai Mathematical Journal

Gaps in the exponent spectrum of subgroups of discrete quasiconformal groups

Petra Bonfert-Taylor, Kurt Falk, and Edward C. Taylor

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Abstract

Let G be a discrete quasiconformal group preserving B3 whose limit set Λ(G) is purely conical and all of ∂B3. Let Ĝ be a non-elementary normal subgroup of G: we show that there exists a set $\mathcal{A}$ of full measure in Λ(G) so that $\mathcal{A}$, regarded as a subset of Λ (Ĝ), has "fat horospherical" dynamics relative to Ĝ. As an application we will bound from below the exponent of convergence of Ĝ in terms of the Hausdorff dimension of $\mathcal{A}$.

Article information

Source
Kodai Math. J. Volume 31, Number 1 (2008), 68-81.

Dates
First available in Project Euclid: 25 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1206454552

Digital Object Identifier
doi:10.2996/kmj/1206454552

Mathematical Reviews number (MathSciNet)
MR2414234

Zentralblatt MATH identifier
1148.30025

Citation

Bonfert-Taylor, Petra; Falk, Kurt; Taylor, Edward C. Gaps in the exponent spectrum of subgroups of discrete quasiconformal groups. Kodai Math. J. 31 (2008), no. 1, 68--81. doi:10.2996/kmj/1206454552. https://projecteuclid.org/euclid.kmj/1206454552.


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