Abstract
In this paper, we establish Basmajian’s identity for certain (1,1,2)-hyperconvex Anosov representations from a free group into [Formula: see text]. We then study our series identities on holomorphic families of Cantor non-conformal repellers associated to complex (1,1,2)-hyperconvex Anosov representations. We show that the series is absolutely summable 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.
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