Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable analytic vector fields with a nilpotent linear part   We study the normalization of integrable analytic vector fields with a
nilpotent linear part. We prove that such an analytic vector field can be
transformed into a certain form by convergent transformations when it has a
non-singular formal integral. In particular, we show that a formally
linearizable analytic vector field with a nilpotent linear part is linearizable
by convergent transformations. We then prove that there are smoothly
linearizable parabolic analytic transformations which cannot be embedded into
the flow of any analytic vector field with a nilpotent linear part.

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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics