The Spectrum of a Hyperbolic Evolution Operator

We study the time T-map U which maps initial data (u0, u1) to the solution and its derivative (u(T), ut(T)) of the homogeneous wave equation in a domain with time T-periodic boundary. The spectrum of U and the type of the spectrum are completely analyzed. The spectrum is the unit circle if a certain rotation number is irrational. It is a full annulus if this rotation number is rational and a weak additional assumption is satisfied.