Multifractal properties of snapshot attractors of random maps

Details Multifractal properties of snapshot attractors of random maps Multifractal properties of snapshot attractors of random maps

Jan 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phrva..41..784r&link_type=abstract

Physical Review A - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 3rd Series (ISSN 0556-2791), vol

Mathematics

Probability

41

Fractals, Liapunov Functions, Random Processes, Strange Attractors, Chaos, Dynamic Characteristics, Fluid Flow, Probability Density Functions, Statistical Analysis

Scientific paper

Qualitative and quantitative properties of 'snapshot attractors' of random maps are considered. A snapshot attractor is the measure resulting from many iterations of a cloud of initial conditions viewed at a single instant. The multifractal properties of these snapshot attractors are studied, using the Liapunov-number partition function method to calculate the spectra of generalized dimensions and of scaling indices. Special attention is devoted to the numerical implementation of scaling indices. 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. The work is relevant to problems in the convection of particles by chaotic fluid flows.

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