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PreprintCC BY 4.0HAL

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, such that the forcing trough the nonlinear dynamics attains a dense subspace on manifolds with and without boundary. Our key argument is the Nachbin’s theorem, which is an analogue of the well-known Stone-Weierstrass the- orem in differentiable spaces. 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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Cite

BibTeXRIS
BibTeX
@misc{buffe2026saturation,
  title = {{Saturation on compact manifolds via Stone-Weierstrass type theorem, and forced nonlinear PDEs}},
  author = {Rémi Buffe and Alessandro Duca and Hugo Parada},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29914},
  eprint = {2610.29914},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05800260v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Saturation on compact manifolds via Stone-Weierstrass type theorem, and forced nonlinear PDEs
AU  - Rémi Buffe
AU  - Alessandro Duca
AU  - Hugo Parada
PY  - 2026
DA  - 2026/10/09
PB  - HAL
DO  - 10.48550/arxiv.2610.29914
UR  - https://hal.science/hal-05800260v1
AB  - We consider polynomial nonlinear PDEs on compact manifolds with finite-dimensional forcing terms. We provide necessary and sufficient conditions, such that the forcing trough the nonlinear dynamics attains a dense subspace on manifolds with and without boundary. Our key argument is the Nachbin’s theorem, which is an analogue of the well-known Stone-Weierstrass the- orem in differentiable spaces. As applications, we prove small-time approximate controllability by additive finite-dimensional controls, topological irreducibility and almost sure unboundedness of Sobolev norms.
ER  -