MULTIFRACTAL PROPERTIES OF SNAPSHOT ATTRACTORS OF RANDOM MAPS

被引:106
作者
ROMEIRAS, FJ
GREBOGI, C
OTT, E
机构
[1] INST SUPER TECN, CTR ELECTRODINAM INIC, P-1096 LISBON, PORTUGAL
[2] UNIV MARYLAND, DEPT PHYS, COLLEGE PK, MD 20742 USA
来源
PHYSICAL REVIEW A | 1990年 / 41卷 / 02期
关键词
D O I
10.1103/PhysRevA.41.784
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We consider qualitative and quantitative properties of snapshot attractors of random maps. By a random map we mean that the parameters that occur in the map vary randomly from iteration to iteration according to some probability distribution. By a snapshot attractor we mean the measure resulting from many iterations of a cloud of initial conditions viewed at a single instant (i.e., iteration). In this paper we investigate the multifractal properties of these snapshot attractors. In particular, we use the Lyapunov number partition function method to calculate the spectra of generalized dimensions and of scaling indices for these attractors; special attention is devoted to the numerical implementation of the method and the evaluation of statistical errors due to the finite number of sample orbits. This work was motivated by problems in the convection of particles by chaotic fluid flows. © 1990 The American Physical Society.
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页码:784 / 799
页数:16
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