Summary: We consider a linear hyperbolic system with constant coefficients with nonlinear boundary conditions and consistent initial conditions. According A. N. Sharkovsky, Yu. L. Maistrenko and E.Yu. Romanenko [Difference equations and their applications, Kluwer Academic Publishers (1993)] the solution of this problem can be written via iterated maps of the interval. These maps characterize the evolution of vector fields given by the boundary value problem. The configurations of the streamlines of this vector field depend on the periodic orbits structure of the interval maps.
Our objective is to characterize the dynamics of these maps using symbolic dynamics and to compute some topological invariants.