Symbolic dynamics in boundary value problem for systems with two spatial variables

Abstract

We consider a linear hyperbolic system with constant coe cients with nonlinear boundary conditions and consistent initial conditions. According Sharkovsky et al in [6] the solution of this problem can be written via iterated maps of the interval. These maps characterize the evolution of vector fi elds given by the boundary value problem. The confi gurations of the streamlines of this vector field depends 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.