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Erschienen in:
2018 | OriginalPaper | Buchkapitel
3. Exponential Dichotomies: Discrete Time
verfasst von : Luís Barreira, Davor Dragičević, Claudia Valls
Erschienen in: Admissibility and Hyperbolicity
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Abstract
In this chapter we start discussing the admissibility theory in the general case of exponential dichotomies. The objective is the same—to characterize the notion of an exponential dichotomy in terms of an admissibility property. The arguments build substantially on those in Chapter 2, although there are various technical difficulties that need to be overcome to treat the general case. The major difficulty consists of showing that an admissibility property implies the existence of contracting and expanding directions, with invertibility along the unstable direction. In this chapter we consider only the case of discrete time. In Chapter 4 we develop a corresponding theory for continuous time.