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Nonuniform Dichotomy Spectrum Intervals: Theorem and Computation
Hailong Zhu,Zhaoxiang Li
Keywords:Lyapunov exponents;Nonuniform exponential dichotomy spectrum;Spectrum Intervals; Weak integral separation.
Abstract:
      In this paper, on the condition of nonuniformly bounded growth, we give the relationship between the nonuniform exponential dichotomy spectrum and the other two classical spectrums (the Lyapunov spectrum and Sacker-Sell spectrum), present their stability, under small linear perturbations. The main goal of this paper is to discuss the theory for the computation of these spectrums on the condition of nonuniformly bounded growth, and this extends the work of Dieci and Vleck \cite{dv-02}, which computes the Lyapunov spectrum and Sacker-Sell spectrum under the condition of bounded. Finally, the numerical examples are given to illustrate and verify the theoretical results.