Dans cette thèse, on étudie des marches aléatoires induites par des actions de groupes probabilisés sur des espaces de courbure négative ou nulle. On décrit en particulier le cas d'actions sur des espaces CAT(0) admettant des éléments contractants, c'est-à-dire dont les propriétés imitent ceux des isométries loxodromiques dans les espaces Gromov-hy...
Subshifts are sets of colourings-or tilings-of the plane, defined by local constraints. Historically introduced as discretizations of continuous dynamical systems, they are also heavily related to computability theory. In this article, we study a conjugacy invariant for subshifts, known as the projective fundamental group and we show that any finit...
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics, engineering, medicine to economics. These systems are impossible to be properly modelled and simulated with standard Ordinary Differential Equations (ODE), or any data-driven approximation including Neural Ordinary Differe...
The aim of the poster is to showcase the interplay between group theory, algebraic topology and combinatorics on words. A result that allows to display this is the return theorem by Berté et al. in 2015. The poster will contain an introduction to fundamental groups of graphs, dendric words as well as a new result concerning return groups of eventua...
Since 2015, dendric shifts (a generalisation of Sturmian words) have been widely studied. One of the results concerning these shift spaces is the return theorem. It describes the groups generated by the return words of a dendric shift. The proof uses the fundamental group of the Rauzy graph of the shift space. Later, eventually dendric shifts were ...
National audience
When confronted with an ever-changing and often perilous environment, how an organism behaves in response to uncertain and incomplete sensory information can be a matter of life and death. Besides the need to assess individual sensory signals accurately, sensory systems must also be able to integrate signals from multiple sensory modalities (e.g. v...
The use of the Koopman operator framework in dynamical systems has greatly expanded in recent years. Instead of considering the evolution of the state of a system, the Koopman semigroup tracks the evolution of observables on the state. Since the Koopman operator defined for an arbitrary dynamical system is linear, it allows us to use linear system ...
Coupled Oscillator Systems (COS) are presented as a method for sound synthesis and musical instrumentation. Seven systems ranging in size from 3 to 9 oscillators are described with different arrangements all containing a topology of velocity based coupling terms. First, each system is described mathematically. Then, each system is analyzed with rec...
An exposition of Vyugin's proof of ergodic theorem and its application to algorithmic randomness
