Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fatou components of attracting skew products   We investigate the existence of wandering Fatou components for polynomial
skew-products in two complex variables. In 2004 the non-existence of wandering
domains near a super-attracting invariant fiber was shown in [8]. In 2014 it
was shown in [1] that wandering domains can exist near a parabolic invariant
fiber. In [9] the geometrically-attracting case was studied, and we continue
this study here. We prove the non-existence of wandering domains for
subhyperbolic attracting skew products; this class contains the maps studied in
[9]. Using expansion properties on the Julia set in the invariant fiber, we
prove bounds on the rate of escape of critical orbits in almost all fibers. Our
main tool in describing these critical orbits is a possibly singular
linearization map of unstable manifolds.

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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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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: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: math-ph