Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable manifolds of two-dimensional biholomorphisms asymptotic to formal
  curves   Let $F\in\mathrm{Diff}(\mathbb{C}^2,0)$ be a germ of a holomorphic
diffeomorphism and let $\Gamma$ be an invariant formal curve of $F$. Assume
that the restricted diffeomorphism $F|_{\Gamma}$ is either hyperbolic
attracting or rationally neutral non-periodic (these are the conditions that
the diffeomorphism $F|_{\Gamma}$ should satisfy, if $\Gamma$ were convergent,
in order to have orbits converging to the origin). Then we prove that $F$ has
finitely many stable manifolds, either open domains or parabolic curves,
consisting of and containing all converging orbits asymptotic to $\Gamma$. Our
results generalize to the case where $\Gamma$ is a formal periodic curve of
$F$.

4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph