Local models for smooth vector fields of the line

Stavros Anastassiou

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arXiv · 2407.15091

Local models for smooth vector fields of the line

Stavros Anastassiou

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Abstract

We present the local classification of singularities of smooth vector fields on the line, with respect to the equivalence relation of $C^1$--conjugacy. Along the way, we recall the analogous classification, up to $C^0$ and $C^{\infty}$ conjugacy. We also give the transversal unfoldings of the corresponding normal forms and treat the case where the changes of coordinates are tangent to the identity. Thus, a fairly complete description of the $1$--d case is achieved.

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Stavros Anastassiou. 2024-07-21. Local models for smooth vector fields of the line. https://arxiv.org/abs/2407.15091

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