Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakly mixing diffeomorphisms preserving a measurable Riemannian metric
  are dense in $\mathcal{A}_{\alpha}\left(M\right)$ for arbitrary Liouvillean
  number $\alpha$   We show that on any smooth compact connected manifold of dimension $m\geq 2$
admitting a smooth non-trivial circle action $\mathcal{S} =
\left\{S_t\right\}_{t \in \mathbb{R}}$, $S_{t+1}=S_t$, the set of weakly mixing
$C^{\infty}$-diffeomorphisms which preserve both a smooth volume $\nu$ and a
measurable Riemannian metric is dense in $\mathcal{A}_{\alpha} \left(M\right)=
\overline{ \left\{h \circ S_{\alpha} \circ h^{-1} : h \in
\text{Diff}^{\infty}\left(M, \nu\right) \right\}}^{C^{\infty}}$ for every
Liouvillean number $\alpha$. The proof is based on a quantitative version of
the Anosov-Katok-method with explicitly constructed conjugation maps and
partitions.

3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat