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Dynamical Spectrum for time dependent linear systems in Banach spaces

Abstract:

This paper is primarily concerned with the Dynamical Spectrum for time dependent linear differential equations in Banach spaces. We give a characterization of the Dynamical Spectrum which is an extension of the Sacker-Sell Theorem. Also we define the Lyapunov exponents, who measure the decay rate of the solutions of a linear differential equations; we investigate the relation between the Dynamical Spectrum, the Spectral Subbundles associated with the corresponding spectral intervals and the Lyapunov exponents. These problems are treated in the unified setting of a Linear Skew-Product Semiflow. Finally we present some examples of Linear Skew-Product Semiflow arising from time dependent functional differential equations and parabolic partial differential equations. © 1994 JJIAM Publishing Committee.