Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure of partially hyperbolic H\'enon maps   We consider the structure of substantially dissipative complex H\'enon maps
admitting a dominated splitting on the Julia set. The dominated splitting
assumption corresponds to the one-dimensional assumption that there are no
critical points on the Julia set. Indeed, we prove the corresponding
description of the Fatou set, namely that it consists of only finitely many
components, each either attracting or parabolic periodic. In particular there
are no rotation domains, and no wandering components. Moreover, we show that $J
= J^\star$ and the dynamics on $J$ is hyperbolic away from parabolic cycles.

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The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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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: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin