On the dimension of stable solution subspaces of differential equations

The topic of the thesis is the calculation of the dimension of asymptotically stable subspaces of the solution set of a linear system of ordinary differential equations. The history of the problem begins with a result on second order linear scalar equations by a French mathematician, Milloux, in 1934 and continues with Hartman, Coppel, Macki and Muldowney as well as many others in the second half of the 20th century. Qian Wang's PhD dissertation (2008) discusses the question in infinite dimensional spaces. In this study we take the research in two new directions. First, we consider non-homogeneous systems of differential equations. All of the prior results require a priori assumptions of stability on the differential equation. The second new direction taken in the thesis is to make these assumptions only on a subspace of the solutions and extends the possibility of discussing the dimension of the asymptotically stable set to equations that may even be unstable.