# Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions

@article{Borthwick2014SymmetryRO,
title={Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions},
author={David Borthwick and Tobias Weich},
journal={arXiv: Spectral Theory},
year={2014}
}
• Published 23 July 2014
• Mathematics
• arXiv: Spectral Theory
Given a holomorphic iterated function scheme with a finite symmetry group $G$, we show that the associated dynamical zeta function factorizes into symmetry-reduced analytic zeta functions that are parametrized by the unitary irreducible representations of $G$. We show that this factorization implies a factorization of the Selberg zeta function on symmetric $n$-funneled surfaces and that the symmetry factorization simplifies the numerical calculations of the resonances by several orders of…

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