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...