Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharkovskii order for non-wandering points   For a map $f:I \rightarrow I$, a point $x \in I$ is periodic with period $p
\in \mathbb{N}$ if $f^p(x)=x$ and $f^j(x)\not=x$ for all $0<j<p$. When $f$ is
continuous and $I$ is an interval, a theorem due to Sharkovskii (\cite{BC})
states that there is an order in $\mathbb{N}$, say $\lhd$, such that, if $f$
has a periodic point of period $p$ and $p \lhd q$, then $f$ also has a periodic
point of period $q$. In this work, we will see how an extension of this order
$\lhd$ to an ultrapower of the integer numbers yields a Sharkovskii-type result
for non-wandering points of $f$.

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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci