Structure of infinite-dimensional stable canonical equations with periodic coefficients (Q1089492)

The following equation is considered: (1) \(J(dx/dt)=iA(t)x,\) where A(t), \(-\infty <t<\infty\) is a given piecewise continuous periodic function whose values are bounded selfadjoint operators on an infinite dimensional Hilbert space H; the constant operator J is selfadjoint, bounded and invertible. The equation (1) is called strongly stable if the solutions of all nearby equations of the same type are bounded on the real line. Structure of connected components of the set of strongly stable equations is studied. The approach used is based on the properties of the monodromy operator and of the unitary group in H.