8th Croatian Mathematical Congress

On the periods of periodic points in the hyperspace of continua in dimension one

2 Jul 2024, 17:50

20m

D6 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Talk DS/ODE: Dynamical Systems, Ordinary Differential Equations and Applications Dynamical Systems, Ordinary Differential Equations and Applications

Speaker

Domagoj Jelić (University of Split, Faculty of Science)

Description

Whenever we are given a selfmap f of a compact metric space
X, we can associate with it the induced mapping C(f) on the
hyperspace C(X) of continua in X, defined in a natural way.

In this talk we discuss and provide the answer to the following question:
Let f be a selfmap of a topological tree T, and let x be a periodic point of f of given period p. What are the possible periods of periodic points of C(T) containing x?

We will argue the significant importance of this result when studying some other features of the system (C(T),C(f)).
The talk is based on a joint work with Piotr Oprocha.