NONWANDERING SETS OF THE POWERS ON THE CIRCLE

For continuous maps f of the circle to itself, we show that (1) the set of ${\omega}$-limit points is contained in the set of nonwandering points of $f^n$ for all $n{\geq}1$. (2) if the set of turning points of f is finite, then the set of accumulation points of non wandering set is contained in the set of non wandering points of $f^n$ for all $n{\geq}1$.