Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic integrable systems: Analytic normalization and embedding flows   In this paper we mainly study the existence of analytic normalization and the
normal form of finite dimensional complete analytic integrable dynamical
systems. More details, we will prove that any complete analytic integrable
diffeomorphism $F(x)=Bx+f(x)$ in $(\mathbb C^n,0)$ with $B$ having eigenvalues
not modulus $1$ and $f(x)=O(|x|^2)$ is locally analytically conjugate to its
normal form. Meanwhile, we also prove that any complete analytic integrable
differential system $\dot x=Ax+f(x)$ in $(\mathbb C^n,0)$ with $A$ having
nonzero eigenvalues and $f(x)=O(|x|^2)$ is locally analytically conjugate to
its normal form. Furthermore we will prove that any complete analytic
integrable diffeomorphism defined on an analytic manifold can be embedded in a
complete analytic integrable flow. We note that parts of our results are the
improvement of Moser's one in {\it Comm. Pure Appl. Math.} 9$($1956$)$,
673--692 and of Poincar\'e's one in {\it Rendiconti del circolo matematico di
Palermo} 5$($1897$)$, 193--239. These results also improve the ones in {\it J.
Diff. Eqns.} 244$($2008$)$, 1080--1092 in the sense that the linear part of the
systems can be nonhyperbolic, and the one in {\it Math. Res. Lett.}
9$($2002$)$, 217--228 in the way that our paper presents the concrete
expression of the normal form in a restricted case.

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph