Gabriel Fuhrmann

Abstract

Given two continuous self-maps f and g on the interval which have all periodic orbits in common (that is, O(x)={x,f(x),...,f^(p-1)(x)} is a p-periodic orbit of f if and only if it is a p-periodic orbit of g but a priori, f may permute the elements of O(x) in a different fashion than g does), it is natural to ask whether f=g on the closure of the periodic points (which is known to coincide with the closure of the recurrent points!).
We show this is the case wherever orbits with prime periods are dense. Specifically, we show that mixing interval maps are uniquely determined by (the location of) their periodic orbits.
Joint work with Maik Gröger (Jagiellonian University) and Alejandro Passeggi (University of the Republic Uruguay).