Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic Continuity of Metric Entropy for Volume-preserving
  Diffeomorphisms   Let $M$ be a compact manifold and $\text{Diff}^1_m(M)$ be the set of $C^1$
volume-preserving diffeomorphisms of $M$. We prove that there is a residual
subset $\mathcal {R}\subset \text{Diff}^1_m(M)$ such that each $f\in
\mathcal{R}$ is a continuity point of the map $g\to h_m(g)$ from
$\text{Diff}^1_m(M)$ to $\mathbb{R}$, where $h_m(g)$ is the metric entropy of
$g$ with respect to volume measure $m$.

1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ