4 papers
Piecewise rotations: limit set for the non -bijective maps
Nicolas Bédaride, Jean françois Bertazzon, Idrissa Kaboré
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 uppe…
Majoration of the dimension of the space of concatenated solutions of a specific pantograph equation
Jean-François Bertazzon
For each , we consider the integral equation: \[ \int_{λy} ^{λx} f(t)\, d t = f(x) - f(y) \mbox{ for every ,} \] where is the concat…
An example of PET. Computation of the Hausdorff dimension of the aperiodic set
Nicolas Bédaride, Jean-François Bertazzon
We introduce a family of piecewise isometries. This family is similar to the ones studied by Hooper and Schwartz. We prove that a renormalization scheme exists inside this family a…
Minoration of the complexity function associated to a translation on the torus
Nicolas Bédaride, Jean François Bertazzon
We show that the complexity function of a piecewise translation map conjugated to a minimal translation on the torus $\TT^k = \RR^k / \ZZ^k$ is at least for every i…