MAPS OF THE INTERVAL LJAPUNOV STABLE ON THE SET OF NONWANDERING POINTS
V. V. FEDORENKO and J. SMITAL
Abstract.
Any dynamical system generated by a continuous map of the compact unit interval $I$, is Ljapunov stable on the set of $\omega$-limit points iff it is Ljapunov stable on the set of non-wandering points. This and recent known results imply that Ljapunov stability on the set of non-wandering points characterizes maps non-chaotic in the sense of Li and Yorke.
Compressed Postscript 
