Exponential dichotomy, integral separation and diagonalizability of linear systems of ordinary differential equations

AbstractThis paper is concerned with linear systems of ordinary differential equations. A criterion for integral separation in terms of exponential dichotomy is given. As corollaries we obtain the roughness theorem for integral separation and the new result that an upper triangular system on a half-line is integrally separated if and only if the system corresponding to its diagonal is. We then show that a diagonal system on a half-line is integrally separated if and only if a certain perturbed system is diagonalizable. Using this result we are able to deduce that the interior of the set of diagonalizable systems on a half-line is the set of systems with integral separation and that the interior for the whole line is the set of systems which are integrally separated on both half-lines