Continuity in Weak Topology: First Order Linear Systems of ODE  

作　　者：Gang MENG Mei Rong ZHANG 

机构地区：[1]Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第7期1287-1298,共12页数学学报（英文版）

基　　金：supported by National Basic Research Program of China (Grant No. 2006CB805903);National Natural Science Foundation of China (Grant Nos. 10325102 and 10531010)

摘　　要：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 Lp spaces. The continuity results of this paper are a basis to study these quantities in a quantitative way.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 Lp spaces. The continuity results of this paper are a basis to study these quantities in a quantitative way.

关 键 词：EIGENVALUE Dirac operator Lyapunov exponent rotation number CONTINUITY weak topology 

分 类 号：O171[理学—数学] TP271[理学—基础数学]