The Lind Zeta functions of reversal systems of finite order

Sieye Ryu

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arXiv · 1712.03519

The Lind Zeta functions of reversal systems of finite order

Sieye Ryu

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Abstract

A decomposition theorem for the Lind zeta function of a reversal system $(X, T, R)$ of finite order is established. A reversal system can be regarded as an action of a certain group $G$ on $X$. To establish an explicit formula for the Lind zeta function of $(X, T, R)$, we need to consider finite index subgroups $H$ of $G$ with induced actions given by automorphisms or by flips. When the underlying dynamical system $(X, T)$ is either a shift of finite type or a sofic shift, we express the Lind zeta function of $(X, T, R)$ in terms of matrices.

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Sieye Ryu. 2017-12-10. The Lind Zeta functions of reversal systems of finite order. https://arxiv.org/abs/1712.03519

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