Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Virtual Immediate Basins of Newton Maps and Asymptotic Values   Newton's root finding method applied to a (transcendental) entire function
f:C->C is the iteration of a meromorphic function N. It is well known that if
for some starting value z, Newton's method converges to a point x in C, then f
has a root at x. We show that in many cases, if an orbit converges to infinity
for Newton's method, then f has a `virtual root' at infinity. More precisely,
we show that if N has an invariant Baker domain that satisfies some mild
assumptions, then 0 is an asymptotic value for f.
  Conversely, we show that if f has an asymptotic value of logarithmic type at
0, then the singularity over 0 is contained in an invariant Baker domain of N,
which we call a virtual immediate basin. We show by way of counterexamples that
this is not true for more general types of singularities.

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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an