Chaotic systems are highly susceptible to control by using small perturbations to a system constraint. Feedback methods have been applied to taming chaos in magnetoelastic and hydrodynamic systems, electric circuits, lasers, chemical reactions, and tissues of heart and brain in vitro.1 The well-known Ott-Grebogi-Yorke (OGY) algorithm2 and its variations are based on the notion that for controll...

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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 (...

We establish stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations. Our family of random maps need not be close to a fixed map; thus, our results can handle very general driving mechanisms. We consider (i) perturbations via convolutions, (ii) perturbations arising from finite-rank transfer operator approxim...

In the 1920s Warrington Yorke had pioneered the malarial treatment of G.P.I. and neurosyphilis. It was Warrington Yorke who foresaw the dangers of Japanese intervention in the last war, and the overrunning of Java, the major source of the world's supply of quinine. It was his enthusiasm and energy which led the Governments of the U.K. and U.S.A. to provide mepacrine, which had been developed as...

The study of deterministic laws of evolution has characterized the development of science since Newton’s times. Chaos, namely the manifestation of irregular and unpredictable dynamics (not random but look random [1]), entered the debate on determinism at the end of the 19th century with the discovery of sensitivity to initial conditions, meaning that small infinitesimal differences in the initi...