Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical approximation and kernels of nonescaping-hyperbolic components   Let F_n be families of entire functions, holomorphically parametrized by a
complex manifold M. We consider those parameters in M that correspond to
nonescaping-hyperbolic functions, i.e., those maps f in F_n for which the
postsingular set P(f) is a compact subset of the Fatou set F(f) of f. We prove
that if F_n converge to a family F in the sense of a certain dynamically
sensible metric, then every nonescaping-hyperbolic component in the parameter
space of F is a kernel of a sequence of nonescaping-hyperbolic components in
the parameter spaces of F_n. Parameters belonging to such a kernel do not
always correspond to hyperbolic functions in F. Nevertheless, we show that
these functions must be J-stable. Using quasiconformal equivalences, we are
able to construct many examples of families to which our results can be
applied.

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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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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: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc