Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chaos in Newtonian iterations: Searching for zeros which are not there   We show analytically that Newtonian iterations, when applied to a polynomial
equation, have a positive topological entropy. In a specific example of an
attempt to ``find'' the real solutions of the equation $x^2+1=0$, we show that
the Newton method is chaotic. We analytically find the invariant density and
show how this problem relates to that of a piecewise linear map.

2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg