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- W4301465765 abstract "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 Sharkovskiu{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." @default.
- W4301465765 created "2022-10-05" @default.
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- W4301465765 date "2014-11-11" @default.
- W4301465765 modified "2023-10-14" @default.
- W4301465765 title "Forcing and entropy of strip patterns of quasiperiodic skew products in the cylinder" @default.
- W4301465765 doi "https://doi.org/10.48550/arxiv.1411.2759" @default.
- W4301465765 hasPublicationYear "2014" @default.
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