2025/03/24 by Goncharuk, Nataliya
#03E15 #37E35 #54H05 #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2503.18847
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.