# Uniform periodic point growth in entropy rank one

@article{Miles2006UniformPP, title={Uniform periodic point growth in entropy rank one}, author={Richard Miles and Thomas Ward}, journal={arXiv: Dynamical Systems}, year={2006}, volume={136}, pages={359-365} }

We show that algebraic dynamical systems with entropy rank one have uniformly exponentially many periodic points in all directions.

## 6 Citations

### A Note on the Growth of Periodic Points for Commuting Toral Automorphisms

- Mathematics
- 2012

In this note we study the growth of the number of periodic points for non-degenerate actions of commuting hyperbolic toral automorophisms.

### Synchronization points and associated dynamical invariants

- Mathematics
- 2013

This paper introduces new invariants for multiparameter
dynamical systems. This is done by counting the number of points
whose orbits intersect at time n under simultaneous iteration of finitely …

### Directional uniformities, periodic points, and entropy

- Mathematics
- 2015

Dynamical systems generated by $d\ge2$
commuting homeomorphisms (topological $\mathbb{Z}^d$-actions)
contain within them
structures on many scales,
and in particular contain
many actions of…

### Deposited in DRO : 06 October 2015 Version of attached le : Other Peer-review status of attached

- Mathematics
- 2016

Dynamical systems generated by d > 2 commuting homeomorphisms (topological Z-actions) contain within them structures on many scales, and in particular contain many actions of Z for 1 6 k 6 d.…

### Directional zeta functions: Final report

- Mathematics
- 2008

Directional zeta functions detect subdynamics: The main part of this project (Project 1 in the proposal) concerned the relationship between growth properties of periodic points and the directional…

### A directional uniformity of periodic point distribution and mixing

- Mathematics
- 2011

For mixing [\mathbb Z^d] -actions generated by commuting automorphisms of a compact abelian group, we investigate the directional uniformity of the rate of periodic point distribution and mixing.…

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