Noncompact chain recurrence and attraction

Abstract

Both this paper and Chain recurrence and attraction in noncompact spaces, [Ergodic Theory Dynamical Systems (to appear)] are concerned with the question of extending certain results obtained by C. Conley for dynamical systems on compact spaces to systems on arbitrary metric spaces. The basic result is the analogue of Conley’s theorem that characterizes the chain recurrent set of f f in terms of the attractors of f f and their basins of attraction. The point of view taken in the above-mentioned paper was that the given metric was of primary importance rather than the topology that it generated. The purpose of this note is to give results that depend on the topology induced by a metric rather than on the particular choice of the metric.