Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie groups of real analytic diffeomorphisms are $L^1$-regular   Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all
real-analytic diffeomorphisms of $M$, which is modelled on the (DFS)-space
${\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of
time-dependent real-analytic vector fields on $M$ which are integrable
functions in time, and their dependence on the time-dependent vector field.
Notably, we show that the Lie group $G$ is $L^1$-regular in the sense that each
$[\gamma]$ in $L^1([0,1],{\mathfrak g})$ has an evolution which is an
absolutely continuous $G$-valued function on $[0,1]$ and smooth in $[\gamma]$.
As tools for the proof, we develop several new results concerning
$L^p$-regularity of infinite-dimensional Lie groups, for $1\leq p\leq \infty$,
which will be useful also for the discussion of other classes of groups.
Moreover, we obtain new results concerning the continuity and complex
analyticity of non-linear mappings on open subsets of locally convex direct
limits.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph