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Time-changes preserving zeta functions
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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.
American Mathematical Society (AMS)
Title: Time-changes preserving zeta functions
Description:
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.
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