Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Doubly-resonant saddle-nodes in $(\mathbb{C}^{3},0)$ and the fixed
  singularity at infinity in the Painlev\'e equations (part II): sectorial
  normalization   In this work, following [Bit15], we consider analytic singular vector fields
in $(\mathbb{C}^{3},0)$ with an isolated and doubly-resonant singularity of
saddle-node type at the origin. Such vector fields come from irregular
two-dimensional differential systems with two opposite non-zero eigenvalues,
and appear for instance when studying the irregular singularity at infinity in
Painlev{\'e} equations (P\_j), j=I...V , for generic values of the parameters.
Under suitable assumptions, we prove a theorem of analytic nor-malization over
sectorial domains, analogous to the classical one due to Hukuhara-Kimura-Matuda
[HKM61] for saddle-nodes in $(\mathbb{C}^{2},0)$. We also prove that the
normalizing map is essentially unique and weakly Gevrey-1 summable.

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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs