Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of a class of smooth singular flows on $\mathbb T^2$   We study joining rigidity in the class of von Neumann flows with one
singularity. They are given by a smooth vector field $\mathcal{X}$ on $\mathbb
T^2\setminus \{a\}$, where $\mathcal{X}$ is not defined at $a\in \mathbb T^2$.
It follows that the phase space can be decomposed into a (topological disc)
$D_\mathcal{X}$ and an ergodic component $E_\mathcal{X}=\mathbb T^2\setminus
D_\mathcal{X}$. Let $\omega_\mathcal{X}$ be the 1-form associated to
$\mathcal{X}$. We show that if
$|\int_{E_{\mathcal{X}_1}}d\omega_{\mathcal{X}_1}|\neq
|\int_{E_{\mathcal{X}_2}}d\omega_{\mathcal{X}_2}|$, then the corresponding
flows $(v_t^{\mathcal{X}_1})$ and $(v_t^{\mathcal{X}_2})$ are disjoint. It also
follows that for every $\mathcal{X}$ there is a uniquely associated frequency
$\alpha=\alpha_{\mathcal{X}}\in \mathbb T$. We show that for a full measure set
of $\alpha\in \mathbb T$ the class of smooth time changes of
$(v_t^\mathcal{X_\alpha})$ is joining rigid, i.e. every two smooth time changes
are either cohomologous or disjoint. This gives a natural class of flows for
which the answer to a problem of Ratner (Problem 3 in \cite{Rat4}) is positive.

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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn