Chaotic bifurcations along algebraic curves (Q2751643)
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scientific article; zbMATH DE number 1664993
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chaotic bifurcations along algebraic curves |
scientific article; zbMATH DE number 1664993 |
Statements
1 April 2002
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system of iterated maps
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periodic orbits
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logistic family
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nonmonotone orbit-bifurcation structure
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critical point
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chaotic attractor
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antimonotonicity
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Chaotic bifurcations along algebraic curves (English)
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The authors examine some problems of nonmonotone bifurcations for one-parameter families of cubic maps, and rational maps of reals. In particular they present a counterexample to the antimonotonicity conjecture enounced in the paper by \textit{S. Dawson, C. Grebogi, J. Yorke, I. Kan}, and \textit{H. Kocak} [Antimonotonicity: inevitable reversals of period-doubling cascades, Phys. Lett. A 162, 245-254 (1992)] that any one-parameter family of smooth one-dimensional maps has an antimonotone parameter value whenever at least two independent critical points are contained in the interior of a chaotic attractor.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00041].
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