Non-smooth saddle-node bifurcations. I: Existence of an SNA (Q2813943)
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scientific article; zbMATH DE number 6594779
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-smooth saddle-node bifurcations. I: Existence of an SNA |
scientific article; zbMATH DE number 6594779 |
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17 June 2016
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strange non-chaotic attractor
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non-uniformly hyperbolic attractor
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quasi-periodically forced interval maps
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Lyapunov exponent
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Non-smooth saddle-node bifurcations. I: Existence of an SNA (English)
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This paper studies a general one-parameter family of quasi-periodically forced monotone interval maps and proves that some map in the family has a non-uniformly hyperbolic attractor called a strange non-chaotic attractor (SNA) and undergoes a non-smooth saddle-node bifurcation. Similar conclusions for special families of skew products were found by \textit{K. Bjerklöv} [Commun. Math. Phys. 272, No. 2, 397--442 (2007; Zbl 1135.37031)] and \textit{T. H. Jäger} [Mem. Am. Math. Soc. 945, 1--106 (2009; Zbl 1188.37034)]. To obtain his main result on the existence of SNAs, the author of the paper under review links ideas of Bjerklöv [loc. cit.] and Jäger [loc. cit.].
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