a1 Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
a2 Department of Mathematics, Wesleyan University, Middleton, CT 06457, USA
a3 Department of Mathematics, Swarthmore College, Swarthmore, PA 19081, USA
a4 Department of Mathematics, Tufts University, Medford, MA 02155, USA
For continuous maps ƒ of the circle to itself, we show: (A) the set of nonwandering points of ƒ coincides with that of ƒn for every odd n; (B) ƒ has a horseshoe if and only if it has a non-wandering homoclinic point; (C) if the set of periodic points is closed and non-empty, then every non-wandering point is periodic.
(Received January 04 1983)
(Revised May 15 1983)