Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entrainment to Subharmonic Trajectories in Oscillatory Discrete-Time
  Systems   A matrix $A$ is called totally positive (TP) if all its minors are positive,
and totally nonnegative (TN) if all its minors are nonnegative. A square matrix
$A$ is called oscillatory if it is TN and some power of $A$ is TP. A linear
time-varying system is called an oscillatory discrete-time system (ODTS) if the
matrix defining its evolution at each time $k$ is oscillatory. We analyze the
properties of $n$-dimensional time-varying nonlinear discrete-time systems
whose variational system is an ODTS, and show that they have a well-ordered
behavior. More precisely, if the nonlinear system is time-varying and
$T$-periodic then any trajectory either leaves any compact set or converges to
an $(n-1)T$-periodic trajectory, that is, a subharmonic trajectory. These
results hold for any dimension $n$. The analysis of such systems requires
establishing that a line integral of the Jacobian of the nonlinear system is an
oscillatory matrix. This is non-trivial, as the sum of two oscillatory matrices
is not necessarily oscillatory, and this carries over to integrals. We derive
several new sufficient conditions guaranteeing that the line integral of a
matrix is oscillatory, and demonstrate how this yields interesting classes of
discrete-time nonlinear systems that admit a well-ordered behavior.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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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: physics
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con