Generalized Specification Property and Distributional Chaos

Abstract

Let f be a continuous map from a compact interval into itself. Continuing the work begun by Schweizer and Smítal [1994], we prove that the restriction of f to any basic set (i.e. any nonsolenoidal, infinite, maximal ω-limit set) satisfies a generalization of the specification property. We apply this generalization to establish several conjectures made in the abovementioned paper, e.g. the fact that distributional chaos is stable.