arXiv subjects

Idrissa Kaboré

Publications and source records attributed to Idrissa Kaboré.

5 recordsLinked to original sources

arXiv2026

On modulo-recurrence and window complexity in infinite words

In this paper, we introduce the notions of uniform modulo-recurrence and strong modulo-recurrence. We show that Sturmian words and maximal complexity words are strongly modulo-recurrent. Next, a relationship between the window complexity and the classical complexity of the Thue-Morse word is established. We provide an aperiodic recurrent word such that the window complexity is bounded. We also construct a family of aperiodic recurrent words such that their window complexity $P^w(n)$ is in $O(n^α)$, while at least $n^α$ for infinitely many $n$, where $0<α<1$. Finally, we establish that the window complexity of a uniformly recurrent aperiodic word is unbounded.

math.CO↗

arXiv2022

Word of low complexity without uniform frequencies

In this paper, we construct a uniformely recurrent infinite word of low complexity without uniform frequencies of letters. This shows the optimality of a bound of Boshernitzan, which gives a sufficient condition for a uniformly recurrent infinite word to admit uniform frequencies.

math.DS↗

arXiv2022

Piecewise rotations: limit set for the non -bijective maps

We consider non-bijective piecewise rotations of the plane. These maps belong to a family introduced in previous papers by Boshernitzan and Goetz. We derive in this paper some upper bounds to the size of the limit set. This improves results of \cite{Bosh.Goet.03}.

math.DS↗

arXiv2020

Symbolic dynamics for the piecewise rotations: Case of the bijective symmetric maps

We consider a specific %piecewise rotation of the plane that is continuous on two half-planes, class of piecewise rotations of the plane that are continuous on two half-planes, as studied in \cite{Bosh.Goet.03}, \cite{Goet.Quas.09} and \cite{Che.Goe.Qua.12}. %If Assuming that the angle belongs to the set $\{\fracπ{2},\fracπ{3},\fracπ{6},\fracπ{4}\} %$ $, we give a description of the symbolic dynamics of this map in the bijective symmetric case.

math.DS↗

arXiv2017

Symbolic dynamics of a piecewise rotation: case of the non symmetric bijective maps

We consider a specific piecewise rotation of the plane that is continuous on two half-planes, as studied by some authors like Boshernitzan, Goetz and Quas. If the angle belongs to the set $\{\fracπ{2},\frac{2π}{3},\fracπ{4}\}$, we give a complete description of the symbolic dynamics of this map in the non symmetric bijective case.

math.DS↗