The spectrum of a hyperbolic evolution operator
The spectrum of the time \(T\)-map \(U\), which maps initial data \((u(0),u_t(0))\) to \((u(T),u_t(T))\), the solution of the homogeneous wave equation in a domain with time \(T\)-periodic boundary, is completely analyzed. The spectrum is a unit circle if a rotation number is irrational and it is a full annulus if this number is rational and a weak additional assumption is satisfied.
scientific article; zbMATH DE number 850611