Continuity in weak topology: First order linear systems of ODE
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- Meng, G. & Zhang, M.R. Acta. Math. Sin.-English Ser. (2010) 26: 1287. doi:10.1007/s10114-010-8103-x
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In this paper we study important quantities defined from solutions of first order linear systems of ordinary differential equations. It will be proved that many quantities, such as solutions, eigenvalues of one-dimensional Dirac operators, Lyapunov exponents and rotation numbers, depend on the coefficients in a very strong way. That is, they are not only continuous in coefficients with respect to the usual Lp topologies, but also with respect to the weak topologies of the Lp spaces. The continuity results of this paper are a basis to study these quantities in a quantitative way.