Quasiconformal groups, Patterson-Sullivan theory, and local analysis of limit sets

Bonfert-Taylor, Petra; Taylor, Edward

doi:10.1090/S0002-9947-02-03134-3

Quasiconformal groups, Patterson-Sullivan theory, and local analysis of limit sets
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by Petra Bonfert-Taylor and Edward C. Taylor PDF

Trans. Amer. Math. Soc. 355 (2003), 787-811 Request permission

Abstract:

We extend the part of Patterson-Sullivan theory to discrete quasiconformal groups that relates the exponent of convergence of the Poincaré series to the Hausdorff dimension of the limit set. In doing so we define new bi-Lipschitz invariants that localize both the exponent of convergence and the Hausdorff dimension. We find these invariants help to expose and explain the discrepancy between the conformal and quasiconformal setting of Patterson-Sullivan theory.

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