Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cherry flow: physical measures and perturbation theory   In this article we consider Cherry flows on torus which have two
singularities: a source and a saddle, and no periodic orbits. We show that
every Cherry flow admits a unique physical measure, whose basin has full
volume. This proves a conjecture given by R. Saghin and E. Vargas in~\cite{SV}.
We also show that the perturbation of Cherry flow depends on the divergence at
the saddle: when the divergence is negative, this flow admits a neighborhood,
such that any flow in this neighborhood belongs to the following three cases:
(a) has a saddle connection; (b) a Cherry flow; (c) a Morse-Smale flow whose
non-wandering set consists two singularities and one periodic sink. In
contrary, when the divergence is non-negative, this flow can be approximated by
non-hyperbolic flow with arbitrarily larger number of periodic sinks.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int