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.
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References
L. Barreira, D. Dragičević, C. Valls, Nonuniform hyperbolicity and admissibility. Adv. Nonlinear Stud. 14, 791–811 (2014)
L. Barreira, D. Dragičević, C. Valls, Nonuniform hyperbolicity and one-sided admissibility. Rend. Lincei Mat. Appl. 27, 235–247 (2016)
L. Barreira, D. Dragičević, C. Valls, Admissibility on the half line for evolution families. J. Anal. Math. 132, 157–176 (2017)
D. Henry, Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, vol. 840 (Springer, Berlin, 1981)
N. Huy, N. Van Minh, Exponential dichotomy of difference equations and applications to evolution equations on the half-line. Comput. Math. Appl. 42, 301–311 (2001)
A. Sasu, B. Sasu, Exponential dichotomy and (ℓ p, ℓ q) -admissibility on the half-line. J. Math. Anal. Appl. 316, 397–408 (2006)
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Barreira, L., Dragičević, D., Valls, C. (2018). Exponential Dichotomies: Discrete Time. In: Admissibility and Hyperbolicity. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-90110-7_3
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DOI: https://doi.org/10.1007/978-3-319-90110-7_3
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