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arXiv · 2602.21159

Global hypoellipticity for perturbations of complex vector fields on the torus

Maria V. Bartmeyer·Paulo L. Dattori da Silva·Rafael B. Gonzalez
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Abstract

We apply Kr\"{o}necker's approximation theorem to measure (in a topological sense) a set of constants which turn a vector field into a non-globally hypoelliptic operator. We present situations in which this set is a discrete enumerable (hence, meager) subset of the real line, and we also show that this set may be a dense $\mathcal{G}_\delta$ subset of the complex numbers (hence, nonmeager), which produces a contrast to a known result stating that this set has null Lebesgue measure.

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Maria V. Bartmeyer, Paulo L. Dattori da Silva, Rafael B. Gonzalez. 2026-02-24. Global hypoellipticity for perturbations of complex vector fields on the torus. https://arxiv.org/abs/2602.21159

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