Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalization of singular contact forms and primitive 1-forms   A differential 1-form $\alpha$ on a manifold of odd dimension $2n+1$, which
satisfies the contact condition $\alpha \wedge (d\alpha)^n \neq 0$ almost
everywhere, but which vanishes at a point $O$, i.e. $\alpha (O) = 0$, is called
a \textit{singular contact form} at $O$. The aim of this paper is to study
local normal forms (formal, analytic and smooth) of such singular contact
forms. Our study leads naturally to the study of normal forms of singular
primitive 1-forms of a symplectic form $\omega$ in dimension $2n$, i.e.
differential 1-forms $\gamma$ which vanish at a point and such that $d\gamma =
\omega$, and their corresponding conformal vector fields. Our results are an
extension and improvement of previous results obtained by other authors, in
particular Lychagin \cite{Lychagin-1stOrder1975}, Webster
\cite{Webster-1stOrder1987} and Zhitomirskii
\cite{Zhito-1Form1986,Zhito-1Form1992}. We make use of both the classical
normalization techniques and the toric approach to the normalization problem
for dynamical systems \cite{Zung_Birkhoff2005, Zung_Integrable2016,
Zung_AA2018}.

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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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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: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex