Towards a Polya-Carlson dichotomy for algebraic dynamics

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.

References in corpus (3)

• Dirichlet series for finite combinatorial rank dynamics
• Dynamical invariants for group automorphisms
• Automorphisms with exotic orbit growth

Cited by in corpus (5)

• Dold sequences, periodic points, and dynamics
• Dynamics on abelian varieties in positive characteristic
• A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus
• Dynamical zeta functions of Reidemeister type and representations spaces
• The dynamical zeta function for commuting automorphisms of zero-dimensional groups