A quasiperiodically forced skew-product on the cyclinder without fixed-curves
In [FJJK] the Sharkovskiı 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 Sharkovskiı Theorem holds when restricted to curves instead of general strips? We an...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:169487 |
| Acceso en línea: | https://ddd.uab.cat/record/169487 https://dx.doi.org/urn:doi:10.1016/j.na.2016.08.011 |
| Access Level: | acceso abierto |
| Palabra clave: | Invariant strips Quasiperiodically forced systems on the cylinder |
| Sumario: | In [FJJK] the Sharkovskiı 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 Sharkovskiı Theorem holds 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. [FJJK] Roberta Fabbri, Tobias Jäger, Russell Johnson, and Gerhard Keller. A Sharkovskii-type theorem for minimally forced interval maps. Topol. Methods Nonlinear Anal., 26(1):163--188, 2005. |
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