Time-changes preserving zeta functions

Sawian Jaidee, Patrick Moss, Tom Ward

Research output: Contribution to journalArticle

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Abstract

We associate to any dynamical system with finitely many periodic orbits of each period a collection of possible time-changes of the sequence of periodic point counts for that specific system that preserve the property of counting periodic points for some system. 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 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.

Original languageEnglish
Pages (from-to)4425-4438
Number of pages14
JournalProceedings of the American Mathematical Society
Volume147
Issue number10
Early online date10 Jun 2019
DOIs
Publication statusPublished - 2019

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