Abstract
We give a classification of generic vector fields near a generic submanifold. The normal forms are linear vector fields near the local model of the submanifold. Similar results are obtained for vector fields near a hypersurface with boundary and near a piecewise-smooth hypersurface.
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Ishikawa, G., Izumiya, S. & Watanabe, K. Vector fields near a generic submanifold. Geom Dedicata 48, 127–137 (1993). https://doi.org/10.1007/BF01264065
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DOI: https://doi.org/10.1007/BF01264065