Time-changes preserving zeta functions
Dynamical Systems
2020-11-30 v2 Number Theory
Abstract
We associate to any dynamical system with finitely many periodic orbits of each length a collection of possible time-changes of the sequence of periodic point counts that preserve the property of counting periodic points. Intersecting over all dynamical systems gives a monoid of time-changes that have this property for all such systems. We show that the only polynomials lying in this `universally good' monoid are the monomials, and that this monoid is uncountable. Examples give some insight into how the structure of the collection of maps varies for different dynamical systems.
Cite
@article{arxiv.1809.09199,
title = {Time-changes preserving zeta functions},
author = {Sawian Jaidee and Patrick Moss and Tom Ward},
journal= {arXiv preprint arXiv:1809.09199},
year = {2020}
}
Comments
Updated version with typos fixed and more explanations