Numbers, computers and dynamical systems

A discrete dynamical system is defined as a set of states on which a transformation acts, considered as an evolution rule. The terminology discrete refers to the time that is discretized: at time n corresponds the nth iteration of this transformation.
Dynamical systems are widely studied, for their modelling as well as for their computation power.

We will focus here more specifically on trajectories of chaotic dynamical system from a computer science viewpoint (finite or periodic trajectories). A classical example is provided by the links between the Gauss map, continued fractions and Euclid’s algorithm. We will also consider various application fields such as discrete geometry, quasicrystals, or else, computer arithmetics.