Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forcing and entropy of strip patterns of quasiperiodic skew products in
  the cylinder   We extend the results and techniques from \cite{FJJK} to study the
combinatorial dynamics (\emph{forcing}) and entropy of quasiperiodically forced
skew-products on the cylinder. For these maps we prove that a cyclic
permutation $\tau$ forces a cyclic permutation $\nu$ as interval patterns if
and only if $\tau$ forces $\nu$ as cylinder patterns. This result gives as a
corollary the Sharkovski\u{\i} Theorem for quasiperiodically forced
skew-products on the cylinder proved in \cite{FJJK}.
  Next, the notion of $s$-horseshoe is defined for quasiperiodically forced
skew-products on the cylinder and it is proved, as in the interval case, that
if a quasiperiodically forced skew-product on the cylinder has an $s$-horseshoe
then its topological entropy is larger than or equals to $\log(s).$
  Finally, if a quasiperiodically forced skew-product on the cylinder has a
periodic orbit with pattern $\tau,$ then $h(F) \ge h(f_{\tau}),$ where
$f_{\tau}$ denotes the \emph{connect-the-dots} interval map over a periodic
orbit with pattern $\tau.$ This implies that if the period of $\tau$ is $2^n q$
with $n \ge 0$ and $q \ge 1$ odd, then $h(F) \ge \tfrac{\log(\lambda_q)}{2^n}$,
where $\lambda_1 = 1$ and, for each $q \ge 3,$ $\lambda_q$ is the largest root
of the polynomial $x^{q} - 2x^{q-2} - 1.$ Moreover, for every $m=2^n q$ with $n
\ge 0$ and $q \ge 1$ odd, there exists a quasiperiodically forced skew-product
on the cylinder $F_m$ with a periodic orbit of period $m$ such that $h(F_m) =
\tfrac{\log(\lambda_q)}{2^n}.$ This extends the analogous result for interval
maps to quasiperiodically forced skew-products on the cylinder.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: eess