Anti-classification results for smooth dynamical systems. Preliminary Report
Dynamical Systems
2022-06-22 v1 Logic
Abstract
The paper considers the equivalence relation of conjugacy-by-homeomorphism on diffeomorphisms of smooth manifolds. In dimension 2 and above it is shown that there is no Borel method of attaching complete numerical invariants. In dimension 5 and above it is shown that the equivalence relation is not Borel, and in fact is complete analytic.
Cite
@article{arxiv.2206.09322,
title = {Anti-classification results for smooth dynamical systems. Preliminary Report},
author = {Matthew Foreman and Anton Gorodetski},
journal= {arXiv preprint arXiv:2206.09322},
year = {2022}
}