A quasiperiodically forced skew-product on the cyclinder without fixed-curves
Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Morales, Leopoldo (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2008-01486 Ministerio de Economía y Competitividad MTM2011-26995-C02-01 Ministerio de Economía y Competitividad MTM2014-52209-C2-1
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Invariant strips ; Quasiperiodically forced systems on the cylinder
Published in:	Nonlinear Analysis : Theory, Methods and Applications, Vol. 145 (2016) , p. 199-263, ISSN 0362-546X

DOI: 10.1016/j.na.2016.08.011

Postprint 62 p, 2.3 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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