Specification and $\ddot{I}‰$-chaos in non-compact systems

Abstract

In this paper, we demonstrate conditions under which a Lindelöf dynamical system exhibits $\ddot{I}‰$-chaos. In particular, if a system exhibits a generalized version of the specification property and has at least three points with mutually separated orbit closures, then the system exhibits dense $\ddot{I}‰$-chaos.