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Nonuniform dichotomy spectrum and reducibility for nonautonomous equations. (English) Zbl 1344.37038

Summary: 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.

MSC:

37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37B55 Topological dynamics of nonautonomous systems
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