On the structural stability relative to the space of linear differential equations with periodic coefficients

Let ω LEn be the Banach space of linear non-homogeneous differential equations of order n with -periodic coefficients. We prove the following statements. The equation l LEnω is structurally stable in the phase space Φn : Rn  R / ωZ (n  2) if and only if its multiplicators do not belong to the unit circle. The set of all structurally stable equations is everywhere dense in ω LEn. The equation 2 ω l LE is structurally stable in the phase space Φ2 : RP2  R / ωZ if and only if its multiplicators are real, different and distinct from 1. We describe also the topological equivalence classis of structurally stable in  2 equations.