Stability of Lyapunov Exponents, Weak Integral Separation and Nonuniform Dichotomy Spectrum

Abstract: In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system are proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical one. Furthermore, the existence of full nonuniform exponential dichotomy spectrum under the condition of weak integral separateness is also presented.