Equivalence of Equicontinuity and Distality for Real Non-autonomous systems

Abstract

In this paper, we investigate equicontinuity and distality for non-autonomous systems on the interval. We investigate distality of the system using the enveloping cover $E_0(X)=\overline{\{\omega_k:k\in \Z \}}$. We prove that if a sequence of homeomorphisms on the interval $(f_n)$ converges to an injective function then the sequence $(f_n^{-1})$ converges to a continuous surjective function. Consequently, we establish equivalence of distality and equicontinuity for non-autonomous systems on the interval.