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Basmajian-type identities and Hausdorff dimension of limit sets

Research paper by Yan Mary He

Indexed on: 19 Feb '16Published on: 19 Feb '16Published in: Mathematics - Dynamical Systems



Abstract

In this paper, we study Basmajian-type series identities on holomorphic families of Cantor sets associated to one-dimensional complex dynamical systems. We show that the series is absolutely summable if and only if the Hausdorff dimension of the Cantor set is strictly less than one. Throughout the domain of convergence, these identities can be analytically continued and they exhibit nontrivial monodromy.