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arXiv · 2610.29914

Saturation on compact manifolds via Stone-Weierstrass type theorem, and forced nonlinear PDEs

Rémi Buffe·Alessandro Duca·Hugo Parada
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Abstract

We consider polynomial nonlinear PDEs on compact manifolds with finite-dimensional forcing terms. We provide necessary and sufficient conditions under which the forcing, through the nonlinear dynamics, attains a dense subspace on manifolds with and without boundary. Our key argument is Nachbin's theorem, which is an analogue of the well-known Stone-Weierstrass theorem in spaces of differentiable functions. As applications, we prove small-time approximate controllability by additive finite-dimensional controls, topological irreducibility, and almost sure unboundedness of Sobolev norms.

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Rémi Buffe, Alessandro Duca, Hugo Parada. 2026-10-21. Saturation on compact manifolds via Stone-Weierstrass type theorem, and forced nonlinear PDEs. https://arxiv.org/abs/2610.29914

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