Lyapunov exponents for linear delay equations in arbitrary phase spaces - Markus Riedle (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2002)
A linear differential equation with infinite delay is considered in the generalized form as an integral equation. As usually, the function space ß of the admissible initial conditions is only described axiomatically. Merely using this abstract 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 ß. The representation requires a modified version of the usual weak* -integral.
urn:nbn:de:kobv:11-10049188
Keywords: 330; Lyapunov exponents; differential equations with infinite delay; weak* -integral; abstract phase space; variation of constants formula; stochastic delay differential equations