On the relation of seven chaos characterizations

Abstract

In this work, we explore seven chaos-related notions in dynamical systems: locally everywhere onto, mixing, totally transitive, strong dense periodicity, blending, specification, and Devaney chaos. We analyze their interrelations, proving positive connections and providing counterexamples for negative ones. Our findings establish a hierarchy among these chaos characterizations, with the specification property at the top and blending, transitivity, and strong dense periodicity at the bottom in compact spaces. In shifts of finite type, these properties are equivalent, but this equivalence does not hold in shifts of infinite type.