A Unified Theory of Proportion
An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation
An extension of Markov partitions for a certain toral endomorphism.
Arithmetic on blocks.
Asynchronous sliding block maps
Asynchronous sliding block maps
We define a notion of asynchronous sliding block map that can be realized by transducers labeled in A* × B*. We show that, under some conditions, it is possible to synchronize this transducer by state splitting, in order to get a transducer which defines the same sliding block map and which is labeled in A × Bk, where k is a constant integer. In the case of a transducer with a strongly connected graph, the synchronization process can be considered as an implementation of an algorithm of...
Attracteurs, orbites et ergodicité
Attracting dynamics of exponential maps.
Automate des préfixes-suffixes associé à une substitution primitive
On explicite une conjugaison en mesure entre le décalage sur le système dynamique associé à une substitution primitive et une transformation adique sur le support d'un sous-shift de type fini, à savoir l'ensemble des chemins d'un automate dit des préfixes-suffixes. En caractérisant les préimages par la conjugaison des chemins périodiques de l'automate, on montre que cette conjugaison est injective sauf sur un ensemble dénombrable, sur lequel elle est finie-à-un. On en déduit l'existence d'une suite...
Automatic sequences generated by synchronizing automata fulfill the Sarnak conjecture
We prove that automatic sequences generated by synchronizing automata satisfy the full Sarnak conjecture. This is of particular interest, since Berlinkov proved recently that almost all automata are synchronizing.
Basic properties of shift radix systems.
Best simultaneous diophantine approximations of some cubic algebraic numbers
Let be a real algebraic number of degree over whose conjugates are not real. There exists an unit of the ring of integer of for which it is possible to describe the set of all best approximation vectors of .’
Beta-expansions with negative bases.
Beta-numbers whose conjugates lie near the unit circle
Billiard complexity in the hypercube
We consider the billiard map in the hypercube of . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that is the order of magnitude of the complexity.
Borel isomorphism of SPR Markov shifts
We show that strongly positively recurrent Markov shifts (including shifts of finite type) are classified up to Borel conjugacy by their entropy, period and their numbers of periodic points.
Bounds for graph expansions via elasticity.
Bouquets of circles for lamination languages and complexities
Laminations are classic sets of disjoint and non-self-crossing curves on surfaces. Lamination languages are languages of two-way infinite words which code laminations by using associated labeled embedded graphs, and which are subshifts. Here, we characterize the possible exact affine factor complexities of these languages through bouquets of circles, i.e. graphs made of one vertex, as representative coding graphs. We also show how to build families of laminations together with corresponding lamination...
-algebras associated with presentations of subshifts.
Calcul de la dynamique de transformations linéaires contractantes mod 1 et arbre de Farey