Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The partial captivity condition for U(1) extensions of expanding maps on
  the circle   This paper concerns the compact group extension \[ f:\mathbb{T}^2\to
\mathbb{T}^2,\quad f (x,s)= (E(x), s+\tau(x)\ \text{mod }1) \] of an expanding
map $E:\mathbb{S}^1\to \mathbb{S}^1$. The dynamics of $f$ and its stochastic
perturbations have previously been studied under the so-called partial
captivity condition. Here we prove a supplementary result that shows that
partial captivity is a $\mathscr{C}^r$ generic condition on $\tau$, once we fix
$E$.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex