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Basmajian-type identities and Hausdorff dimension of limit sets

Published online by Cambridge University Press:  14 March 2017

YAN MARY HE
YAN MARY HE*
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA email he@math.uchicago.edu
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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 non-trivial monodromy.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 6 , September 2018 , pp. 2224 - 2244
Copyright
© Cambridge University Press, 2017 

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