Abstract
This chapter discusses the stability of noncompact sets in semidynamical systems (SDSs.). These systems are continuous flows defined for all future time (non-negative t). The chapter presents the natural examples of SDSs by functional differential equations for which existence and uniqueness conditions hold. SDSs offer new and interesting notions which are not possible in dynamical systems. The chapter discusses limit sets and prolongations and their limit sets. For a rim-compact space, t each of positive limit set and prolongational limit is weakly negatively invariant and contains no start points; moreover if the prolongational limit set is nonempty and compact, so is the positive limit set. The chapter also describes stability and asymptotic stability.
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