TY - JOUR

T1 - Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point

AU - Alsedá, Lluís

AU - Llibre, Jaume

AU - Misiurewicz, Michał

AU - Simó, Carles

PY - 1985/1/1

Y1 - 1985/1/1

N2 - 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. © 1985, Cambridge University Press. All rights reserved.

AB - 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. © 1985, Cambridge University Press. All rights reserved.

U2 - https://doi.org/10.1017/S0143385700003126

DO - https://doi.org/10.1017/S0143385700003126

M3 - Article

VL - 5

SP - 501

EP - 517

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

ER -