Abstract
We study the time T-map U which maps initial data ( u 0, u 1) to the solution and its derivative ( u( T), u t ( 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.
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