Acta Mathematica Sinica, English Series

, Volume 26, Issue 7, pp 1287–1298

Continuity in weak topology: First order linear systems of ODE


DOI: 10.1007/s10114-010-8103-x

Cite this article as:
Meng, G. & Zhang, M.R. Acta. Math. Sin.-English Ser. (2010) 26: 1287. doi:10.1007/s10114-010-8103-x


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.


eigenvalue Dirac operator Lyapunov exponent rotation number continuity weak topology 

MR(2000) Subject Classification

34A30 34L40 37E45 34D08 58C07 

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingP. R. China