Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperchaotic attractors of three-dimensional maps and scenarios of their
  appearance   We study bifurcation mechanisms of the appearance of hyperchaotic attractors
in three-dimensional maps. We consider, in some sense, the simplest cases when
such attractors are homoclinic, i.e. they contain only one saddle fixed point
and entirely its unstable manifold. We assume that this manifold is
two-dimensional, which gives, formally, a possibility to obtain two positive
Lyapunov exponents for typical orbits on the attractor (hyperchaos). For
realization of this possibility, we propose several bifurcation scenarios of
the onset of homoclinic hyperchaos that include cascades of both supercritical
period-doubling bifurcations with saddle periodic orbits and supercritical
Neimark-Sacker bifurcations with stable periodic orbits, as well as various
combinations of these cascades. In the paper, these scenarios are illustrated
by an example of three-dimensional Mir\'a map.

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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas