Topological classification of complex linear systems

In this paper we show that a complex linear system Σ(A,B) : dx/dz = Ax + Bu, z is a an element of C is linearly equivalent to a canonical direct product of the simple linear systems. After, we prove that two systems are topologically equivalent ↔ holomorphically equivalent ↔ linearly equivalent ↔ the components in their canonical direct products are the same. Then we give a necessary condition such that two uncontrollable systems are topologically equivalents. (author). 21 refs