Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The unstable set of a periodic orbit for delayed positive feedback   In the paper [Large-amplitude periodic solutions for differential equations
with delayed monotone positive feedback, JDDE 23 (2011), no. 4, 727--790], we
have constructed large-amplitude periodic orbits for an equation with delayed
monotone positive feedback. We have shown that the unstable sets of the
large-amplitude periodic orbits constitute the global attractor besides
spindle-like structures. In this paper we focus on a large-amplitude periodic
orbit $\mathcal{O}_{p}$ with two Floquet multipliers outside the unit circle,
and we intend to characterize the geometric structure of its unstable set
$\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$. We prove that
$\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$ is a three-dimensional
$C^{1}$-submanifold of the phase space and admits a smooth global graph
representation. Within $\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$, there
exist heteroclinic connections from $\mathcal{O}_{p}$ to three different
periodic orbits. These connecting sets are two-dimensional $C^{1}$-submanifolds
of $\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$ and homeomorphic to the
two-dimensional open annulus. They form $C^{1}$-smooth separatrices in the
sense that they divide the points of
$\mathcal{W}^{u}\left(\mathcal{O}_{p}\right)$ into three subsets according to
their $\omega$-limit sets.

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The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom