This paper investigates dynamical systems arising from the action by translations on the orbit closures of self-similar and self-aane tilings of R d : The main focus is on spectral properties of such… (More)

We study self-similar sets with overlaps, on the line and in the plane. It is shown that there exist self-similar sets that have non-integral Hausdorr dimension equal to the similarity dimension, but… (More)

It is natural to expect that the arithmetic sum of two Cantor sets should have positive Lebesgue measure if the sum of their dimensions exceeds 1, but there are many known counterexamples, e.g. when… (More)

A bstract . The distribution νλ of the random series ∑ ±λn has been studied by many authors since the two seminal papers by Erdős in 1939 and 1940. Works of Alexander and Yorke, Przytycki and… (More)

1. Lenz and Stollman [3] pointed out that the “metric” ρ defined on page 266 of [4] does not satisfy the triangle inequality. There we used for two Delone sets Λ1 and Λ2, denoting by Br the ball of… (More)

The distribution of the random series P n is the innnite convolution product of 1 2 (? n + n). These measures have been studied since the 1930's, revealing connections with harmonic analysis, the… (More)

We consider two dynamical systems associated with a substitution of Pisot type: the usual Zaction on a sequence space, and the R-action, which can be defined as a tiling dynamical system or as a… (More)

We study parabolic iterated function systems with overlaps on the real line. We show that if a d-parameter family of such systems satisfies a transversality condition, then for almost every parameter… (More)

There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite… (More)