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Power law asymptotics in the creation of strange attractors in the quasi-periodically forced quadratic family
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2017 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 30, no 12, p. 4483-4522Article in journal (Refereed) Published
Abstract [en]

Let Phi be a quasi-periodically forced quadratic map, where the rotation constant omega is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under Phi) attracting graph of a nowhere continuous measurable function psi from the circle T to [0, 1]. This paper investigates how a smooth attractor degenerates into a strange one, as a parameter beta approaches a critical value beta(0), and the asymptotics behind the bifurcation of the attractor from smooth to strange. In our model, the cause of the strange attractor is a so-called torus collision, whereby an attractor collides with a repeller. Our results show that the asymptotic minimum distance between the two colliding invariant curves decreases linearly in the parameter beta, as beta approaches the critical parameter value beta(0) from below. Furthermore, we have been able to show that the asymptotic growth of the supremum of the derivative of the attracting graph is asymptotically bounded from both sides by a constant times the reciprocal of the square root of the minimum distance above.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2017. Vol. 30, no 12, p. 4483-4522
Keywords [en]
dynamical systems, strange attractors, quasi-periodic quadratic family, bifurcations, asymptotics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-219325DOI: 10.1088/1361-6544/aa8c9eISI: 000415852200001Scopus ID: 2-s2.0-85036637885OAI: oai:DiVA.org:kth-219325DiVA, id: diva2:1162673
Funder
Swedish Research Council, 2012-3090
Note

QC 20171205

Available from: 2017-12-05 Created: 2017-12-05 Last updated: 2017-12-19Bibliographically approved

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Timoudas, Thomas Ohlson

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