Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coexistence phenomena in the H\'enon family   We study the classical H\'enon family $f_{a,b}:(x,y)\mapsto(1-ax^2+y,bx)$,
$0<a<2$, $0<b<1$, and prove that given an integer $k\geq 1$, there is a set of
parameters $E_k$ of positive two-dimensional Lebesgue measure so that
$f_{a,b}$, for $(a,b)\in E_k$, has at least $k$ attractive periodic orbits and
one strange attractor. A corresponding statement also holds for the
H\'enon-like families. The final main result of the paper is the existence,
within the classical H\'enon family, of a positive Lebesgue measure set of
parameters whose corresponding maps have two coexisting strange attractors.

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The categories of this paper are: patt-sol
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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: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc