31 citations · 184 across the 16 of their papers we have counts for
16 papers
A dynamical zeta function for group actions
Richard Miles
This article introduces and investigates the basic features of a dynamical zeta function for group actions, motivated by the classical dynamical zeta function of a single transform…
The dynamical zeta function for commuting automorphisms of zero-dimensional groups
Richard Miles, Thomas Ward
For a -action by commuting homeomorphisms of a compact metric space, Lind introduced a dynamical zeta function that generalizes the dynamical zeta function of a s…
Directional uniformities, periodic points, and entropy
Richard Miles, Thomas Ward
Dynamical systems generated by commuting homeomorphisms (topological -actions) contain within them structures on many scales, and in particular contain many a…
Towards a Polya-Carlson dichotomy for algebraic dynamics
Jason Bell, Richard Miles, Thomas Ward
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 functio…
Dynamical invariants for group automorphisms
Richard Miles, Matthew Staines, Thomas Ward
We discuss some of the issues that arise in attempts to classify automorphisms of compact abelian groups from a dynamical point of view. In the particular case of automorphisms of…
A directional uniformity of periodic point distribution and mixing
R. Miles, T. Ward
For mixing~-actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distributi…