Talk by Ed Ott, Maryland – Niels Bohr Institute - University of Copenhagen

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Talk by Ed Ott, Maryland


How certain can we be that an attractor is chaotic: Universal parameter scaling of chaos versus periodicity

The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount can convert an attractor from chaotic to non-chaotic or vice-versa. We call a parameter value where this can happen -uncertain. The probability that a random choice of the parameter is -uncertain commonly scales like a power law in . Surprisingly, two seemingly similar ways of  defining this scaling, both of physical interest, yield different numerical values for the scaling exponent. We show why this happens and present a quantitative analysis of this phenomenon.