Anti-classification for flows on two-tori
Dynamical Systems
2025-05-12 v2 Logic
Abstract
We prove that the classification of real-analytic vector fields on the two-torus up to orbital topological equivalence does not admit a complete numerical invariant that is a Borel function. Moreover, smooth vector fields that are difficult to classify appear in generic smooth 7-parameter families. In dimension 2, this improves the recent result of Gorodetski and Foreman (arXiv:2206.09322) for non-classifiability of smooth diffeomorphisms up to continuous conjugacy.
Cite
@article{arxiv.2503.18847,
title = {Anti-classification for flows on two-tori},
author = {Nataliya Goncharuk},
journal= {arXiv preprint arXiv:2503.18847},
year = {2025}
}