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arXiv · 2503.18847

Anti-classification for flows on two-tori

Nataliya Goncharuk
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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.

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Nataliya Goncharuk. 2025-03-24. Anti-classification for flows on two-tori. https://arxiv.org/abs/2503.18847

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