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oai:recercat.cat:2072/4457532024-12-20T05:14:56Zcom_2072_199267com_2072_4427col_2072_201036

00925njm 22002777a 4500 dc Alsedà, L. author Mañosas, F. author Morales, L. author 2016-01-01 In Fabbri et al. (2005) the Sharkovskiĭ Theorem was extended to periodic orbits of strips of quasiperiodic skew products in the cylinder. In this paper we deal with the following natural question that arises in this setting: Does Sharkovskiĭ Theorem hold when restricted to curves instead of general strips? We answer this question in the negative by constructing a counterexample: We construct a map having a periodic orbit of period 2 of curves (which is, in fact, the upper and lower circles of the cylinder) and without any invariant curve. In particular this shows that there exist quasiperiodic skew products in the cylinder without invariant curves. © 2016 Elsevier Ltd http://hdl.handle.net/2072/445753 10.1016/j.na.2016.08.011 A quasiperiodically forced skew-product on the cylinder without fixed-curves