29 citations · 98 across the 37 of their papers we have counts for
7 papers · 1 filter
Properties of a random Cantor set with overlaps
Anna Chiara Lai, Paola Loreti
We study the topology and the Hausdorff dimension of a random Cantor set with overlaps, generated by an iterated function system with scaling ratio equal to the Golden Mean. The re…
Gap estimates for the spectrum of -bonacci numbers
Anna Chiara Lai, Paola Loreti
We establish some results on the structure of the spectrum of -bonacci numbers. More precisely, we study explicit lower bounds for the distance between elements separated by …
Optimal expansions of Kakeya sequences
Anna Chiara Lai, Paola Loreti
We investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they…
Fibonacci Expansions
Claudio Baiocchi, Vilmos Komornik, Paola Loreti
Expansions in the Golden ratio base have been studied since a pioneering paper of Rényi more than sixty years ago. We introduce closely related expansions of a new type, based on t…
Solutions of fractional logistic equations by Euler's numbers
Mirko D'Ovidio, Paola Loreti
In this paper, we solve in the convergence set, the fractional logistic equation making use of Euler's numbers. To our knowledge, the answer is still an open question. The key poin…
Optimal expansions in non-integer bases
Karma Dajani, Martijn de Vries, Vilmos Komornik +1
For a given positive integer , let and . A sequence consisting of elements in is called an expansion of if $\sum_{i…