Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of periodic orbits near heteroclinic connections   We consider a potential $W:R^m\rightarrow R$ with two different global minima
$a_-, a_+$ and, under a symmetry assumption, we use a variational approach to
show that the Hamiltonian system \begin{equation} \ddot{u}=W_u(u), \hskip 2cm
(1) \end{equation} has a family of $T$-periodic solutions $u^T$ which, along a
sequence $T_j\rightarrow+\infty$, converges locally to a heteroclinic solution
that connects $a_-$ to $a_+$. We then focus on the elliptic system
\begin{equation} \Delta u=W_u(u),\;\; u:R^2\rightarrow R^m, \hskip 2cm (2)
\end{equation} that we interpret as an infinite dimensional analogous of (1),
where $x$ plays the role of time and $W$ is replaced by the action functional
\[J_R(u)=\int_R\Bigl(\frac{1}{2}\vert u_y\vert^2+W(u)\Bigr)dy.\] We assume that
$J_R$ has two different global minimizers $\bar{u}_-, \bar{u}_+:R\rightarrow
R^m$ in the set of maps that connect $a_-$ to $a_+$. We work in a symmetric
context and prove, via a minimization procedure, that (2) has a family of
solutions $u^L:R^2\rightarrow R^m$, which is $L$-periodic in $x$, converges to
$a_\pm$ as $y\rightarrow\pm\infty$ and, along a sequence
$L_j\rightarrow+\infty$, converges locally to a heteroclinic solution that
connects $\bar{u}_-$ to $\bar{u}_+$.

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The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat