is a useful tool for numerical studies of the measure, since the measure of any reasonable set may be obtained as the line integral of F around the boundary. We give an effective algorithm for computing F when is a self-similar measure, based on a Laurent expansion of F for large z and a transformation law (Theorem 2.2) for F that encodes the self-similarity of . Using this algorithm we compute...

In recent years, there has been considerable interest among people to use short message service (SMS) as one of the essential and straightforward communications services on mobile devices. The increased popularity of this service also increased the number of mobile devices attacks such as SMS spam messages. SMS spam messages constitute a real problem to mobile subscribers; this worries telecomm...

In this paper, we provide a framework for calculating expected utility in models with chaotic equilibria and consequently a framework for ranking chaos. Suppose that a dynamic economic model’s equilibria correspond to orbits generated by a chaotic dynamical system f : X → X where X is a compact metric space and f is continuous. The map f could represent the forward dynamics xt+1 = f(xt) or the ...

We investigate the prevalence of Li-Yorke pairs for C and C multimodal maps f with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If f is topologically mixing and has no Cantor attractor, then typical (...