Papers by W. Desch and E.D. Sontag

A measurable function x from a subset J of R into a metric space X is said to be C-meagre if C is non-empty subset of X and, for every closed subset K of X disjoint from C, the preimage of K under x has finite Lebesgue measure. This concept of meagreness, applied to trajectories, is shown to provide a unifying framework which facilitates a variety of characterizations, extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems.