Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Specifying attracting cycles for Newton maps of polynomials   We show that for any set of n distinct points in the complex plane, there
exists a polynomial p of degree at most n+1 so that the corresponding Newton
map, or even the relaxed Newton map, for p has the given points as a
super-attracting cycle. This improves the result due to Plaza and Romero
(2011), which shows how to find such a polynomial of degree 2n. Moreover we
show that in general one cannot improve upon degree n+1. Our methods allow us
to give a simple, constructive proof of the known result that for each cycle
length n at least 2 and degree d at least 3, there exists a polynomial of
degree d whose Newton map has a super-attracting cycle of length n.

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The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int