Continuity in weak topology: First order linear systems of ODE
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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 L p topologies, but also with respect to the weak topologies of the L p spaces. The continuity results of this paper are a basis to study these quantities in a quantitative way.
Keywordseigenvalue Dirac operator Lyapunov exponent rotation number continuity weak topology
MR(2000) Subject Classification34A30 34L40 37E45 34D08 58C07
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