Arithmetic properties of the number of periodic points

Abstract: The talk will be of expository character and is based on a joint survey paper with Grzegorz Graff and Thomas Ward. Given a dynamical system, we may consider the sequence counting the number of periodic points of given order (if finite). (Equivalently, this information can be given in terms of the dynamical zeta function of the system.) We will discuss some arithmetic properties of the class of sequences that can be obtained in this manner. Many of such results have been independently rediscovered by various mathematicians working in multiple fields.

In the latter part of the talk, we will also discuss some more recent results concerning the growth rate of the number of periodic points in certain systems of algebraic origin, and obtained in a joint work with Gunther Cornelissen and Marc Houben.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University