# Lyapunov exponents for linear delay equations in arbitrary phase spaces

Riedle, Markus (2005) Lyapunov exponents for linear delay equations in arbitrary phase spaces. Integral Equations and Operator Theory, 54 (2). pp. 259-278. ISSN 0378-620x

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## Abstract

A linear integral equation with infinite delay is considered where the admissible function space $$\mathcal{B}$$ of initial conditions is as usually only described axiomatically. Merely using this axiomatic description, the long time behavior of the solutions is determined by calculating the Lyapunov exponents. The calculation is based on a representation of the solution in the second dual space of $$\mathcal{B}$$ and on a connection between the asymptotic behavior of the solutions of the integral equation under consideration and its adjoint equation subject to the spectral decomposition of the space of initial functions. We apply the result to an example of a stochastic differential equation with infinite delay.

Item Type: Article Lyapunov exponents - differential equations with infinite delay - weak*-integral - abstract phase space - variation of constants formula - stochastic differential equations with delay MSC 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations Ms Lucy van Russelt 19 Nov 2007 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/907

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