Ergodic Theory and Dynamical Systems · 1986 · 43 citations · 7 references
Natural SciencesMathematicsDynamical SystemsGeometryTopologyContinuous Dynamical SystemsContinuous SystemsFixed PointsPeriodic OrbitsTopological DynamicsCircle MapsPeriodic Orbit TheoryPeriodic PointsTopological Transitivity
Abstract We study the dynamics of continuous maps of the circle with periodic points. We show that the centre is the closure of the periodic points and that the depth of the centre is at most two. We also characterize the property that every power is transitive in terms of transitivity of a single power and some periodic data.
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