Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spiralling dynamics near heteroclinic networks   There are few explicit examples in the literature of vector fields exhibiting
complex dynamics that may be proved analytically. We construct explicitly a
{two parameter family of vector fields} on the three-dimensional sphere
$\EU^3$, whose flow has a spiralling attractor containing the following: two
hyperbolic equilibria, heteroclinic trajectories connecting them {transversely}
and a non-trivial hyperbolic, invariant and transitive set. The spiralling set
unfolds a heteroclinic network between two symmetric saddle-foci and contains a
sequence of topological horseshoes semiconjugate to full shifts over an
alphabet with more and more symbols, {coexisting with Newhouse phenonema}. The
vector field is the restriction to $\EU^3$ of a polynomial vector field in
$\RR^4$. In this article, we also identify global bifurcations that induce
chaotic dynamics of different types.

23
The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex