A non-Borel special alpha-limit set in the square

Abstract

We consider the complexity of special $\alpha$-limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necessarily Borel, even in the case of a surjective map on the unit square. This answers a question posed by Kolyada, Misiurewicz, and Snoha.

See https://www.youtube.com/watch?v=Ugwkg8mT7y8 for a short video explaining this paper