English

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

Dynamical Systems 2020-11-12 v1 Logic

Abstract

We consider the complexity of special α\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.

Cite

@article{arxiv.2011.05509,
  title  = {A non-Borel special alpha-limit set in the square},
  author = {Steve Jackson and Bill Mance and Samuel Roth},
  journal= {arXiv preprint arXiv:2011.05509},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T20:04:06.675Z