Denker, Manfred
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Denker, Manfred
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Denker, Manfred
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Item type:Publication, Fractal Curvature Measures and Minkowski Content for Limit Sets of Conformal Function Systems(2011-12-19); ; ; We characterise fractal sets arising from conformal iterated function systems and conformal graph directed Markov systems for which the Minkowski content and the fractal curvature measures exist. With this, we generalise studies that have been carried out for invariant sets of iterated function systems consisting of similarities.doctoral thesis710 182 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Distributionale Konvergenzsätze in unendlicher Ergodentheorie(2006-02-24); ; ; Conservative ergodic measure preserving transformations on infinite measure spaces are considered. The asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling-Kac condition are investigated. As applications we derive asymptotic laws for the normalized Kac process and the normalized spent time Kac process. The notion of uniformly returning sets is introduced. For these sets it is proven that if the wandering rate is slowly varying then the normalized spent time Kac process converges strongly distributional to a random variable uniformly distributed on the unit interval.As a number theoretical application the continued fraction digits are considered as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For this process normalized linearly a large deviation asymptotic is proved.doctoral thesis336 144