Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parabolic curves of diffeomorphisms asymptotic to formal invariant
  curves   We prove that if $F$ is a tangent to the identity diffeomorphism at
$0\in\mathbb{C}^2$ and $\Gamma$ is a formal invariant curve of $F$ then there
exists a parabolic curve (attracting or repelling) of $F$ asymptotic to
$\Gamma$. The result is a consequence of a more general one in arbitrary
dimension, where we prove the existence of parabolic curves of a tangent to the
identity diffeomorphism $F$ at $0\in\mathbb{C}^n$ asymptotic to a given formal
invariant curve under some additional conditions, expressed in terms of a
reduction of $F$ to a special normal form by means of blow-ups and
ramifications along the formal curve.

20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
1
The categories of this paper are: cs