V. Komornik

activity

20062026

most citedGreedy and quasi-greedy expansions in non-integer bases

42 citations · 111 across the 34 of their papers we have counts for

collaborators

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15 papers · 1 filter

math.NT2022

Unique double base expansions

Vilmos Komornik, Wolfgang Steiner, Yuru Zou

For two real bases $q_{0}, q_{1} > 1$ , we consider expansions of real numbers of the form $\sum_{k = 1}^{\infty} i_{k} / (q_{i_{1}} q_{i_{2}} \dots q_{i_{k}})$ with $i_{k} \in {0, 1}$ , which we call…

math.NT2021

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…

math.NT2020

Hausdorff distance of univoque sets

Yi Cai, Vilmos Komornik

Expansions in non-integer bases have been investigated abundantly since their introduction by Rényi. It was discovered by Erdős et al. that the sets of numbers with a unique expans…

math.NT2020

Difference of Cantor sets and frequencies in Thue--Morse type sequences

Yi Cai, Vilmos Komornik

In a recent paper, Baker and Kong have studied the Hausdorff dimension of the intersection of Cantor sets with their translations. We extend their results to more general Cantor se…

math.NT2019

Univoque graphs and multiple expansions

Yuru Zou, Jian Lu, Vilmos Komornik

Unique expansions in non-integer bases $q$ have been investigated in many papers during the last thirty years. They are often conveniently generated by labeled directed graphs. In…

math.NT2017

Bases in which some numbers have exactly two expansions

Vilmos Komornik, Derong Kong

In this paper we answer several questions raised by Sidorov on the set $B_{2}$ of bases in which there exist numbers with exactly two expansions. In particular, we prove tha…

math.NT2016

Critical bases for ternary alphabets

Vilmos Komornik, Marco Pedicini

Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant $q^{'} \approx 1.78723$ in non-integer base expansions on two-letter alphabets: in bases $1 < q < q^{'}$ …

math.NT2015★ 10 cited

Hausdorff dimension of univoque sets and Devil's staircase

Vilmos Komornik, Derong Kong, Wenxia Li

We fix a positive integer $M$ , and we consider expansions in arbitrary real bases $q > 1$ over the alphabet ${0, 1, ..., M}$ . We denote by $U_{q}$ the set of real numbers having a uniqu…

math.NT2011

Discrete spectra and Pisot numbers

Shigeki Akiyama, Vilmos Komornik

By the m-spectrum of a real number q>1 we mean the set Y^m(q) of values p(q) where p runs over the height m polynomials with integer coefficients. These sets have been extensively…

math.NT2010

Optimal expansions in non-integer bases

Karma Dajani, Martijn de Vries, Vilmos Komornik +1

For a given positive integer $m$ , let $A = {0, 1, ..., m}$ and $q \in (m, m + 1)$ . A sequence $(c_{i}) = c_{1} c_{2} ...$ consisting of elements in $A$ is called an expansion of $x$ if $\sum_{i…

math.NT2010★ 2 cited

A two-dimensional univoque set

Martijn de Vries, Vilmos Komornik

Let $J \subset R^{2}$ be the set of couples $(x, q)$ with $q > 1$ such that $x$ has at least one representation of the form $x = \sum_{i = 1}^{\infty} c_{i} q^{- i}$ with int…

math.NT2009

Properties of expansions in complex bases

Vilmos Komornik, Paola Loreti

Expansions in noninteger positive bases have been intensively investigated since the pioneering works of Rényi (1957) and Parry (1960). The discovery of surprising unique expansion…

math.NT2009

Generalized golden ratios of ternary alphabets

Vilmos Komornik, Anna Chiara Lai, Marco Pedicini

Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter a…

math.NT2007★ 42 cited

Greedy and quasi-greedy expansions in non-integer bases

Claudio Baiocchi, Vilmos Komornik

We generalize several theorems of Rényi, Parry, Daróczy and Kátai by characterizing the greedy and quasi-greedy expansions in non-integer bases.

math.NT2006★ 3 cited

Unique expansions of real numbers

Martijn de Vries, Vilmos Komornik

It was discovered some years ago that there exist non-integer real numbers $q > 1$ for which only one sequence $(c_{i})$ of integers $c_{i} \in [0, q)$ satisfies the equality $\sum_{i=1}^…