Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely Many Moduli of Stability at the Dissipative Boundary of Chaos   In the family of area-contracting H\'enon-like maps with zero topological
entropy we show that there are maps with infinitely many moduli of stability.
Thus one cannot find all the possible topological types for non-chaotic
area-contracting H\'enon-like maps in a family with finitely many parameters. A
similar result, but for the chaotic maps in the family, became part of the
folklore a short time after H\'enon used such maps to produce what was soon
conjectured to be the first non-hyperbolic strange attractor in $\mathbb{R}^2$.
Our proof uses recent results about infinitely renormalisable area-contracting
H\'enon-like maps; it suggests that the number of parameters needed to
represent all possible topological types for area-contracting H\'enon-like maps
whose sets of periods of their periodic orbits are finite (and in particular
are equal to $\{1,\, 2,\dots,\,2^{n-1}\}$ or an initial segment of this
$n$-tuple) increases with the number of periods. In comparison, among
$C^k$-embeddings of the 2-disk with $k\geq 1$, the maximal moduli number for
non-chaotic but non area-contracting maps in the interior of the set of
zero-entropy is infinite.

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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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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: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin