Measuring Fractals: Comparison of Theory and Experiment on the Global Properties of a Strange Attractor

摘要: This talk will be about how to characterize and measure the properties of fractal sets. It center an experiment by Libchaber, Heslot, Stavans, Glazier which sees onset chaos via period doubling a quasi-periodic behavior in simple hydrodynamic system. The results this compared with theory Feigenbaum, for doubling, that Shenicer, Feigenbaum Kadanoff case. actual comparison is performed using novel way looking at global attractor was first introduced Parisi Frisch. basic device study distribution densities points on attractor. This, turn, estimated, following Procaccia, measuring time it take recurrence within specified distance. same analysis applied experimental data also theoretical models, giving descriptions topological both. are seen agree errors. net result best quantative evidence date universality mechanism.