Existence of a generalized Floquet basis (Q762335)

The equation \(\dot x=A(t)x\), \((x\in C^ n\), \(t\in {\mathbb{R}})\) is considered, A(t) being a T-periodic matrix. The aim of the paper is the study of the space of almost periodic solutions in the sense of Levitan, that of the automorphic and that of the periodic solutions, under the hypothesis that A is periodic in the sense of Levitan. The author constructs the group of periods and his representation in a manner analogous to that used for the construction of the representation of the monodromy operator and obtains an existence theorem of a generalized Floquet base in these spaces.