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SNA’s in the Quasi-Periodic Quadratic Family

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Abstract

We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic (or logistic) map

$$(\theta,x)\mapsto(\theta+\omega,c(\theta)x(1-x))$$

for certain choices of \({c:\mathbb{T} \to [3/2,4]}\) and Diophantine ω.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Kristian Bjerklöv

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  1. Kristian Bjerklöv
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Correspondence to Kristian Bjerklöv.

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Communicated by A. Kupiainen

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Bjerklöv, K. SNA’s in the Quasi-Periodic Quadratic Family. Commun. Math. Phys. 286, 137–161 (2009). https://doi.org/10.1007/s00220-008-0626-y

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  • DOI: https://doi.org/10.1007/s00220-008-0626-y

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