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S. Baker (2019), B. Barany and A. K{a}enm{a}ki (2019) independently showed that there exist iterated function systems without exact overlaps and there are super-exponentially close cylinders at all small levels. We adapt the method of S. Baker and obtain further examples of this type. We prove that for any algebraic number $betage 2$ there exist real numbers $s, t$ such that the iterated function system $$ left {frac{x}{beta}, frac{x+1}{beta}, frac{x+s}{beta}, frac{x+t}{beta}right } $$ satisfies the above property.
We study random walks on a $d$-dimensional torus by affine expanding maps whose linear parts commute. Assuming an irrationality condition on their translation parts, we prove that the Haar measure is the unique stationary measure. We deduce that if $
Complex-valued periodic sequences, u, constructed by Goran Bjorck, are analyzed with regard to the behavior of their discrete periodic narrow-band ambiguity functions A_p(u). The Bjorck sequences, which are defined on Z/pZ for p>2 prime, are unimodul
We show that any equicontractive, self-similar measure arising from the IFS of contractions $(S_{j})$, with self-similar set $[0,1]$, admits an isolated point in its set of local dimensions provided the images of $S_{j}(0,1)$ (suitably) overlap and t
It is known that the heuristic principle, referred to as the multifractal formalism, need not hold for self-similar measures with overlap, such as the $3$-fold convolution of the Cantor measure and certain Bernoulli convolutions. In this paper we stu
For self-similar sets on $mathbb{R}$ satisfying the exponential separation condition we show that the natural projections of shift invariant ergodic measures is equal to $min{1,frac{h}{-chi}}$, where $h$ and $chi$ are the entropy and Lyapunov exponen