TY - JOUR
T1 - Rotation sets for orbits of degree one circle maps
AU - Alsedà, Lluís
AU - Mañosas, Francesc
AU - Chas, Moira
PY - 2002/1/1
Y1 - 2002/1/1
N2 - Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] a notion of F-rotation interval of a point x ∈ S1 was given. In this paper we define and study a new notion of a rotation set of a point which preserves more of the dynamical information contained in the sequences {Fn(y)}n=0∞ than the one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.
AB - Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] a notion of F-rotation interval of a point x ∈ S1 was given. In this paper we define and study a new notion of a rotation set of a point which preserves more of the dynamical information contained in the sequences {Fn(y)}n=0∞ than the one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.
U2 - 10.1142/S0218127402004437
DO - 10.1142/S0218127402004437
M3 - Article
SN - 0218-1274
VL - 12
SP - 429
EP - 437
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
ER -