Nonuniform dichotomy spectrum and reducibility for nonautonomous equations

For nonautonomous linear differential equations with nonuniform hyperbolicity, we introduce a definition for nonuniform dichotomy spectrum, which can be seen as a generalization of Sacker-Sell spectrum. We prove a spectral theorem and use the spectral theorem to prove a reducibility result.
Comment: arXiv admin note: substantial text overlap with arXiv:1402.1599