FRACTAL DIMENSIONS AND F(ALPHA SPECTRUM OF CHAOTIC SETS NEAR CRISES

被引:7
作者
LEVEN, RW
SELENT, M
UHRLANDT, D
机构
[1] Department of Physics, E.-M.-Arndt-University Greifswald, D-17489 Greifswald
关键词
D O I
10.1016/0960-0779(94)90074-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study numerically the behaviour of the generalized dimensions D(q) and the f(alpha) spectrum in dependence on a control parameter in the parametrically driven, damped pendulum. We find a continuous transition of the D(q) of a chaotic attractor near a boundary crisis to those characterizing a chaotic saddle into which the attractor is converted when the crisis occurs. At an interior crisis a chaotic saddle collides with a small chaotic attractor and both chaotic sets merge to a large chaotic attractor. In the vicinity of the crisis-value of the control parameter the D(q) of the large attractor are close to the D(q) of the small attractor for positive q and near to those of the chaotic saddle for non-positive q. Correspondingly. the f(alpha) spectrum of the large chaotic attractor near the crisis-value is very broad and has a typical phase-transition-like shape.
引用
收藏
页码:661 / 676
页数:16
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