A “superfat” chaotic attractor

A 4-variable invertible map with a chaotic attractor is investigated. Hénon's 2-variable map is used to force two weakly dissipative, linear variables. We determined the fractal dimension of the attractor of the 4-variable map to be larger than three, which is in accordance with the Kaplan-York...

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Published inChaos, solitons and fractals Vol. 3; no. 2; pp. 141 - 148
Main Authors Kube, M.C., Rossler, O.E., Hudson, J.L.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.1993
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Abstract A 4-variable invertible map with a chaotic attractor is investigated. Hénon's 2-variable map is used to force two weakly dissipative, linear variables. We determined the fractal dimension of the attractor of the 4-variable map to be larger than three, which is in accordance with the Kaplan-Yorke conjecture. The topological dimension of the attractor, however, is unity on a dense subset, and therefore, presumably on the whole attractor. The present attractor therefore appears to be an example of a “superfat” attractor, which is an attractor with a dimension gap of more than two.
AbstractList A 4-variable invertible map with a chaotic attractor is investigated. Hénon's 2-variable map is used to force two weakly dissipative, linear variables. We determined the fractal dimension of the attractor of the 4-variable map to be larger than three, which is in accordance with the Kaplan-Yorke conjecture. The topological dimension of the attractor, however, is unity on a dense subset, and therefore, presumably on the whole attractor. The present attractor therefore appears to be an example of a “superfat” attractor, which is an attractor with a dimension gap of more than two.
Author Hudson, J.L.
Rossler, O.E.
Kube, M.C.
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Cites_doi 10.1007/BFb0064319
10.1090/S0002-9904-1967-11798-1
10.1088/0031-8949/40/3/030
10.1007/BFb0076428
10.1017/S0143385700002431
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Title A “superfat” chaotic attractor
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