ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 60,   1   (1991)
pp.   11-14

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.

AMS subject classification.  58F08, 26A18; Secondary 58F13, 54H20
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