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Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces

Yuri D. Latushkin·Stephen J. Montgomery-Smith
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Abstract

We present a spectral mapping theorem for continuous semigroups of operators on any Banach space $E$. The condition for the hyperbolicity of a semigroup on $E$ is given in terms of the generator of an evolutionary semigroup acting in the space of $E$-valued functions. The evolutionary semigroup generated by the propagator of a nonautonomous differential equation in $E$ is also studied. A ``discrete'' technique for the investigating of the evolutionary semigroup is developed and applied to describe the hyperbolicity (exponential dichotomy) of the nonautonomuos equation. File Length: 68K

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BibTeXRIS

Yuri D. Latushkin, Stephen J. Montgomery-Smith. 1999-12-06. Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces. https://arxiv.org/abs/math/9307201

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