Propriétés combinatoires des suites définies par le billard dans les triangles pavants

We study some combinatorial properties of the symbolic dynamics of billiard in the isoceles right angle triangle and in the “half equilateral triangle”. In the case of the isoceles right angle triangle, we develop an algorithm to build the coding sequences and we compute the complexity of these sequences when they are not periodic. Rules for building the infinite words coding the billiard trajectories in an “half equilaterial triangle” are also given. Finally, this leads to an algorithm that gives the coding of a point under a rotation with a partition by intervals.