Uniform distrubution, positive trigonometric polynomials and difference sets
Uniformly distributed sequences mod 1 and Cantor's series representation
Uniformly distributed sequences of positive integers in Baire's space
Uniformly Maldistributed Sequences in a Strict Sense.
Unimodular Pisot substitutions and their associated tiles
Let be a unimodular Pisot substitution over a letter alphabet and let be the associated Rauzy fractals. In the present paper we want to investigate the boundaries () of these fractals. To this matter we define a certain graph, the so-called contact graph of . If satisfies a combinatorial condition called the super coincidence condition the contact graph can be used to set up a self-affine graph directed system whose attractors are certain pieces of the boundaries . From this graph...
Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups.
Univoque sets for real numbers
For x ∈ (0,1), the univoque set for x, denoted (x), is defined to be the set of β ∈ (1,2) such that x has only one representation of the form x = x₁/β + x₂/β² + ⋯ with . We prove that for any x ∈ (0,1), (x) contains a sequence increasing to 2. Moreover, (x) is a Lebesgue null set of Hausdorff dimension 1; both (x) and its closure are nowhere dense.
Upper Estimate of Concentration and Thin Dimensions of Measures
We show upper estimates of the concentration and thin dimensions of measures invariant with respect to families of transformations. These estimates are proved under the assumption that the transformations have a squeezing property which is more general than the Lipschitz condition. These results are in the spirit of a paper by A. Lasota and J. Traple [Chaos Solitons Fractals 28 (2006)] and generalize the classical Moran formula.
Utilisation des produits de Riesz pour minorer la dimension de Hausdorff de certains ensembles.