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A note on the fractalization of saddle invariant curves in quasiperiodic systems
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Univ Barcelona, Dept Matemat Aplicada & Anal, Gran Via 585, E-08007 Barcelona, Spain..
2016 (English)In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 9, no 4, 1095-1107 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to describe a new mechanism of destruction of saddle invariant curves in quasiperiodically forced systems, in which an invariant curve experiments a process of fractalization, that is, the curve gets increasingly wrinkled until it breaks down. The phenomenon resembles the one described for attracting invariant curves in a number of quasiperiodically forced dissipative systems, and that has received the attention in the literature for its connections with the so-called Strange Non-Chaotic Attractors. We present a general conceptual framework that provides a simple unifying mathematical picture for fractalization routes in dissipative and conservative systems.

Place, publisher, year, edition, pages
2016. Vol. 9, no 4, 1095-1107 p.
Keyword [en]
Breakdown of saddle invariant curves, quasiperiodic systems
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-308036DOI: 10.3934/dcdss.2016043ISI: 000384764300011OAI: oai:DiVA.org:uu-308036DiVA: diva2:1049247
Available from: 2016-11-24 Created: 2016-11-23 Last updated: 2016-11-24Bibliographically approved

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Figueras, Jordi-Lluis
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