Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Averaging and rates of averaging for uniform families of deterministic
  fast-slow skew product systems   We consider families of fast-slow skew product maps of the form
\begin{align*} x_{n+1} = x_n+\epsilon a(x_n,y_n,\epsilon), \quad y_{n+1} =
T_\epsilon y_n, \end{align*} where $T_\epsilon$ is a family of nonuniformly
expanding maps, and prove averaging and rates of averaging for the slow
variables $x$ as $\epsilon\to0$. Similar results are obtained also for
continuous time systems \begin{align*} \dot x = \epsilon a(x,y,\epsilon), \quad
\dot y = g_\epsilon(y). \end{align*} Our results include cases where the family
of fast dynamical systems consists of intermittent maps, unimodal maps (along
the Collet-Eckmann parameters) and Viana maps.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
1
The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org