A quasiperiodically forced skew-product on the cylinder without fixed-curves

作者：Alseda Lluis; Manosas Francesc; Morales Leopoldo^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2016, 145: 199-263.

DOI：10.1016/j.na.2016.08.011

• Quasiperiodically forced systems on the cylinder
• Invariant strips

In Fabbri et al. (2005) the Sharkovskii 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 Sharkovskii 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.

• 出版日期2016-11