Towards a Polya-Carlson dichotomy for algebraic dynamics

TL;DR

This paper explores a dichotomy in algebraic dynamics, proposing that dynamical zeta functions of compact group automorphisms are either rational or have a natural boundary, based on analytic behavior.

Contribution

It introduces a Polya-Carlson dichotomy framework for understanding the analytic properties of dynamical zeta functions in algebraic dynamics.

Findings

Support for the dichotomy between rationality and natural boundary behavior

Background rationale for the proposed dichotomy

Results indicating the conditions under which each case occurs

Abstract

We present results and background rationale in support of a Polya--Carlson dichotomy between rationality and a natural boundary for the analytic behaviour of dynamical zeta functions of compact group automorphisms.