On the eigenmodes of periodic orbits for multiple scattering problems in 2D

•Description of an equilibrium state of sound wave reflections between multiple scattering obstacles.•Computation of the asymptotic behaviour of the equilibrium in the high-frequency limit.•Phase of the waves are computed as eigenfunctions of a coupled integral operator•Simple and recursive scheme for arbitrary number of general 2D objects.•Physical interpretation of phase and illustration of correspondance with Fermat’s principle.