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Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point
Published online by Cambridge University Press: 19 September 2008
Abstract
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Let f be a continuous map from the circle into itself of degree one, having a periodic orbit of rotation number p/q ≠ 0. If (p, q) = 1 then we prove that f has a twist periodic orbit of period q and rotation number p/q (i.e. a periodic orbit which behaves as a rotation of the circle with angle 2πp/q). Also, for this map we give the best lower bound of the topological entropy as a function of the rotation interval if one of the endpoints of the interval is an integer.
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- Copyright © Cambridge University Press 1985
References
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